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-(*
-  File:     Anonymous_PAPP_Lowering.thy
-  Author:   Manuel Eberl, University of Innsbruck 
-*)
-section \<open>Lowering P-APP Rules to Smaller Settings\<close>
-theory Anonymous_PAPP_Lowering
-  imports Anonymous_PAPP
-begin
-
-text \<open>
-  In this section, we prove a number of lemmas (corresponding to Lemma~1 in the paper) that allow
-  us to take an anonymous P-APP rule with some additional properties (typically
-  Cardinality-Strategyproofness and Weak Representation or Weak Proportional Representation) and 
-  construct from it an anonymous P-APP rule for a different setting, i.e.\ different number of
-  voters, parties, and/or result committee size.
-
-  In the reverse direction, this also allows us to lift impossibility results from one setting 
-  to another.
-\<close>
-
-subsection \<open>Preliminary Lemmas\<close>
-
-context card_stratproof_anon_papp
-begin
-
-text \<open>
-  The following lemma is obtained by applying Strategyproofness repeatedly. It shows that
-  if we have \<open>l\<close> voters with identical approval lists, then this entire group of voters has no
-  incentive to submit wrong preferences. That is, the outcome they obtain by submitting their 
-  genuine approval lists is weakly preferred by them over all outcomes obtained where these \<open>l\<close>
-  voters submit any other preferences (and the remaining $n - l$ voters submit the same preferences
-  as before).
-
-  This is stronger than regular Strategyproofness, where we only demand that no voter has an
-  incentive to submit wrong preferences \<^emph>\<open>unilaterally\<close> (and everyone else keeps the same
-  preferences). Here we know that the entire group of \<open>l\<close> voters has no incentive to submit
-  wrong preferences in coordination with one another.
-\<close>
-lemma proposition2:
-  assumes "size B = l" "size A + l = n_voters"
-  assumes "X \<noteq> {}" "X \<subseteq> parties" "{} \<notin># A+B" "\<forall>X'\<in>#A+B. X' \<subseteq> parties"
-  shows   "r (replicate_mset l X + A) \<succeq>[Comm(X)] r (B + A)"
-  using assms
-proof (induction l arbitrary: A B)
-  case 0
-  thus ?case
-    by simp
-next
-  case (Suc l A B)
-  from Suc.prems have "set_mset B \<noteq> {}"
-    by auto
-  then obtain Y where Y: "Y \<in># B"
-    by blast
-  define B' where "B' = B - {#Y#}"
-  define A' where "A' = A + {#Y#}"
-  have [simp]: "size B' = l"
-    using Suc.prems Y by (simp add: B'_def size_Diff_singleton)
-  have [simp]: "size A' = n_voters - l"
-    using Suc.prems Y by (simp add: A'_def)
-
-  have "r (B' + A') \<preceq>[Comm(X)] r (replicate_mset l X + A')"
-    by (rule Suc.IH) (use Suc.prems Y in \<open>auto simp: A'_def B'_def size_Diff_singleton\<close>)
-  also have "B' + A' = B + A"
-    using Y by (simp add: B'_def A'_def)
-  also have "r (replicate_mset l X + A') \<preceq>[Comm(X)] r (replicate_mset (Suc l) X + A)"
-  proof (rule not_manipulable'')
-    show "replicate_mset (Suc l) X + A + {#Y#} = replicate_mset l X + A' + {#X#}"
-      by (simp add: A'_def)
-  next
-    show "is_pref_profile (replicate_mset (Suc l) X + A)"
-     using Suc.prems by unfold_locales (auto split: if_splits)
-  next
-    show "is_pref_profile (replicate_mset l X + A')"
-      using Suc.prems Y by unfold_locales (auto split: if_splits simp: A'_def)
-  qed
-  finally show ?case .
-qed
-
-end
-
-
-context card_stratproof_weak_rep_anon_papp
-begin
-
-text \<open>
-  In a setting with Weak Representation and Cardinality-Strategyproofness, Proposition 2 allows
-  us to strengthen Weak Representation in the following way: Suppose we at least 
-  $l \lfloor n/k\rfloor$ voters with the same approval list \<open>X\<close>, and \<open>X\<close> consists of at least \<open>l\<close>
-  parties. Then at least \<open>l\<close> of the members of the result committee are in \<open>X\<close>.
-\<close>
-lemma proposition3:
-  assumes "is_pref_profile A" "X \<subseteq> parties" "card X \<ge> l"
-  assumes "committee_size > 0"
-  assumes "count A X \<ge> l * \<lceil>n_voters / committee_size\<rceil>"
-  shows   "size {# x\<in># r A. x \<in> X #} \<ge> l"
-  using assms
-proof (induction l arbitrary: A X rule: less_induct)
-  case (less l A X)
-  interpret A: anon_papp_profile n_voters parties committee_size A
-    by fact
-  consider "l = 0" | "l = 1" | "l > 1"
-    by force
-  thus ?case
-  proof cases
-    assume "l = 0"
-    thus ?thesis by simp
-  next
-    assume [simp]: "l = 1"
-    define n where "n = count A X"
-    with less.prems have "X \<noteq> {}"
-      by auto
-    then obtain x where x: "x \<in> X"
-      by blast
-    have "n \<le> size A"
-      unfolding n_def by (rule count_le_size)
-    hence "n \<le> n_voters"
-      by (simp add: A.size_A)
-
-    have "count A X > 0"
-      by (rule Nat.gr0I) (use n_voters_pos less.prems in \<open>auto simp: field_simps\<close>)
-    hence "X \<in># A"
-      by force
-    have [simp]: "replicate_mset n X \<subseteq># A"
-      by (simp add: n_def flip: count_le_replicate_mset_subset_eq)
-
-    define A'' where "A'' = A - replicate_mset n X"
-    define A' where "A' = A'' + replicate_mset n {x}"
-    interpret A': anon_papp_profile n_voters parties committee_size A'
-      using A.A_nonempty A.A_subset A.size_A x \<open>X \<in># A\<close>
-      by unfold_locales
-         (fastforce simp: A'_def A''_def size_Diff_submset subset_mset.add_increasing2 
-                    split: if_splits dest!: in_diffD)+
-
-    have "x \<in># r A'"
-    proof (rule weak_representation)
-      show "is_pref_profile A'"
-        by (fact A'.anon_papp_profile_axioms)
-    next
-      have "n_voters \<le> committee_size * n"
-        using less.prems by (simp add: n_def ceiling_le_iff field_simps flip: of_nat_mult)
-      also have "n \<le> count A' {x}"
-        by (simp add: A'_def)
-      finally show "n_voters \<le> committee_size * count A' {x}"
-        by simp
-    qed
-    hence "1 \<le> count (r A') x"
-      by simp
-    also have "\<dots> = size {# y \<in># r A'. y = x #}"
-      by simp
-    also have "\<dots> \<le> size {# y \<in># r A'. y \<in> X #}"
-      by (intro size_mset_mono multiset_filter_mono') (use x in auto)
-
-    also have "r A' \<preceq>[Comm(X)] r A"
-    proof -
-      have "r (replicate_mset n {x} + A'') \<preceq>[Comm(X)] r (replicate_mset n X + A'')"
-      proof (rule proposition2)
-        show "{} \<notin># A'' + replicate_mset n {x}"
-          using A'.A_nonempty by (auto simp: A'_def)
-        show "\<forall>X'\<in>#A'' + replicate_mset n {x}. X' \<subseteq> parties"
-          using A'.A_subset x by (auto simp: A'_def dest: in_diffD)
-        show "size A'' + n = n_voters"
-          using \<open>n \<le> n_voters\<close> by (auto simp: A''_def size_Diff_submset A.size_A)
-      qed (use less.prems in auto)
-      also have "replicate_mset n X + A'' = A"
-        by (simp add: A''_def n_def flip: count_le_replicate_mset_subset_eq)
-      finally show ?thesis
-        by (simp add: A'_def add_ac)
-    qed
-    hence "size {# y \<in># r A'. y \<in> X #} \<le> size {# y \<in># r A. y \<in> X #}"
-      by (simp add: committee_preference_def)
-
-    finally show ?thesis
-      by simp
-
-  next
-    assume l: "l > 1"
-    
-    define n where "n = count A X"
-    have "n \<le> size A"
-      unfolding n_def by (rule count_le_size)
-    hence "n \<le> n_voters"
-      by (simp add: A.size_A)
-
-    define m where "m = nat (ceiling (n_voters / committee_size))"
-    have "n_voters / committee_size \<le> m"
-      unfolding m_def by linarith
-    hence m: "n_voters \<le> committee_size * m"
-      using \<open>committee_size > 0\<close> by (simp add: field_simps flip: of_nat_mult)
-    have "real n_voters / real committee_size > 0"
-      using n_voters_pos less.prems by auto
-    hence m': "\<lceil>real n_voters / real committee_size\<rceil> = int m"
-      by (simp add: m_def)
-    have "1 * m \<le> l * m"
-      using l by (intro mult_right_mono) auto
-    also have "l * m \<le> n"
-      using less.prems by (simp add: m' n_def flip: of_nat_mult)
-    finally have "m \<le> n"
-      by simp
-
-    with less.prems l have "X \<noteq> {}"
-      by auto
-    then obtain x where x: "x \<in> X"
-      by blast
-    have "card (X - {x}) > 0"
-      using less.prems x l by simp
-    hence "X - {x} \<noteq> {}"
-      by force
-
-    have "count A X > 0"
-      by (rule Nat.gr0I) (use n_voters_pos less.prems l in \<open>auto simp: field_simps mult_le_0_iff\<close>)
-    hence "X \<in># A"
-      by force
-    have [simp]: "replicate_mset n X \<subseteq># A"
-      by (simp add: n_def flip: count_le_replicate_mset_subset_eq)
-
-    define A'' where "A'' = A - replicate_mset n X"
-    define A' where "A' = A'' + replicate_mset m {x} + replicate_mset (n - m) (X - {x})"
-    interpret A': anon_papp_profile n_voters parties committee_size A'
-    proof
-      show "Y \<subseteq> parties" if "Y \<in># A'" for Y
-        using that A.A_subset x \<open>X \<in># A\<close>
-        by (fastforce simp: A'_def A''_def dest!: in_diffD split: if_splits)
-    next
-      show "{} \<notin># A'"
-        using A.A_nonempty x \<open>X \<in># A\<close> \<open>X - {x} \<noteq> {}\<close>
-        by (auto simp: A'_def A''_def dest!: in_diffD split: if_splits)
-    next
-      show "size A' = n_voters"
-        using \<open>m \<le> n\<close>
-        by (auto simp: A'_def A''_def A.size_A subset_mset.add_increasing2 size_Diff_submset)
-    qed
-
-    have "x \<in># r A'"
-    proof (rule weak_representation)
-      show "is_pref_profile A'"
-        by (fact A'.anon_papp_profile_axioms)
-    next
-      have "n_voters \<le> committee_size * m"
-        by (fact m)
-      also have "m \<le> count A' {x}"
-        by (simp add: A'_def)
-      finally show "n_voters \<le> committee_size * count A' {x}"
-        by simp
-    qed
-    hence "1 \<le> count (r A') x"
-      by simp
-    also have "\<dots> = size {# y \<in># r A'. y = x #}"
-      by simp
-    finally have 1: "size {#y \<in># r A'. y = x#} \<ge> 1" .
-
-    have 2: "size {# y \<in># r A'. y \<in> X - {x} #} \<ge> l - 1"
-    proof (rule less.IH)
-      have "int (l - 1) * \<lceil>real n_voters / real committee_size\<rceil> = int ((l - 1) * m)"
-        by (auto simp add: m' not_less)
-      also have "(l - 1) * m = l * m - m"
-        by (simp add: algebra_simps)
-      also have "l * m \<le> n"
-        using less.prems by (simp add: m' n_def flip: of_nat_mult)
-      hence "l * m - m \<le> n - m"
-        by (meson diff_le_mono)
-      also have "n - m \<le> count A' (X - {x})"
-        by (simp add: A'_def A''_def)
-      finally show "int (l - 1) * \<lceil>real n_voters / real committee_size\<rceil> \<le> int (count A' (X - {x}))"
-        by simp
-    qed (use l A'.anon_papp_profile_axioms x less.prems in \<open>auto\<close>)
-
-    have "1 + (l - 1) \<le> size {#y \<in># r A'. y = x#} + size {#y \<in># r A'. y \<in> X - {x}#}"
-      by (intro add_mono 1 2)
-    also have "\<dots> = size ({#y \<in># r A'. y = x#} + {#y \<in># r A'. y \<in> X - {x}#})"
-      by simp
-    also have "{#y \<in># r A'. y = x#} + {#y \<in># r A'. y \<in> X - {x}#} =
-               {#y \<in># r A'. y = x \<or> y \<in> X - {x}#}"
-      by (rule filter_mset_disjunction [symmetric]) auto
-    also have "(\<lambda>y. y = x \<or> y \<in> X - {x}) = (\<lambda>y. y \<in> X)"
-      using x by auto
-    also have "1 + (l - 1) = l"
-      using l by simp
-
-    also have "r A' \<preceq>[Comm(X)] r A"
-    proof -
-      have "r (replicate_mset m {x} + replicate_mset (n - m) (X - {x}) + A'') \<preceq>[Comm(X)] 
-            r (replicate_mset n X + A'')"
-      proof (rule proposition2)
-        show " {} \<notin># A'' + (replicate_mset m {x} + replicate_mset (n - m) (X - {x}))"
-          using A'.A_nonempty by (auto simp: A'_def)
-        show "\<forall>X'\<in># A'' + (replicate_mset m {x} + replicate_mset (n - m) (X - {x})). X' \<subseteq> parties"
-          using A'.A_subset x by (auto simp: A'_def dest: in_diffD)
-        show "size A'' + n = n_voters"
-          using \<open>n \<le> n_voters\<close> by (auto simp: A''_def size_Diff_submset A.size_A)
-      qed (use less.prems l \<open>m \<le> n\<close> in auto)
-      also have "replicate_mset n X + A'' = A"
-        by (simp add: A''_def n_def flip: count_le_replicate_mset_subset_eq)
-      finally show ?thesis
-        by (simp add: A'_def add_ac)
-    qed
-    hence "size {# y \<in># r A'. y \<in> X #} \<le> size {# y \<in># r A. y \<in> X #}"
-      by (simp add: committee_preference_def)
-
-    finally show ?thesis
-      by simp
-  qed
-qed
-
-end
-
-
-subsection \<open>Dividing the number of voters\<close>
-
-text \<open>
-  If we have a PAPP rule that satisfies weak representation and cardinality strategyproofness,
-  for $ln$ voters, we can turn it into one for \<open>n\<close> voters.
-  This is done by simply cloning each voter \<open>l\<close> times.
-
-  Consequently, if we have an impossibility result for $n$ voters, it also holds for any
-  integer multiple of \<open>n\<close>.
-\<close>
-locale divide_voters_card_stratproof_weak_rep_anon_papp =
-  card_stratproof_weak_rep_anon_papp "l * n_voters" parties committee_size r
-  for l n_voters parties committee_size r
-begin
-
-definition lift_profile :: "'a set multiset \<Rightarrow> 'a set multiset" where
-  "lift_profile A = (\<Sum>X\<in>#A. replicate_mset l X)"
-
-sublocale lowered: anon_papp_election n_voters parties
-  by standard (use n_voters_pos in auto)
-
-lemma l_pos: "l > 0"
-  using n_voters_pos by auto
-
-lemma empty_in_lift_profile_iff [simp]: "{} \<in># lift_profile A \<longleftrightarrow> {} \<in># A"
-  using l_pos by (auto simp: lift_profile_def)
-
-lemma set_mset_lift_profile [simp]: "set_mset (lift_profile A) = set_mset A"
-  using l_pos by (auto simp: lift_profile_def)
-
-lemma size_lift_profile: "size (lift_profile A) = l * size A"
-  by (simp add: size_mset_sum_mset lift_profile_def image_mset.compositionality o_def)
-
-lemma count_lift_profile [simp]: "count (lift_profile A) x = l * count A x"
-  unfolding lift_profile_def by (induction A) auto
-
-lemma is_pref_profile_lift_profile [intro]:
-  assumes "lowered.is_pref_profile A"
-  shows   "is_pref_profile (lift_profile A)"
-proof -
-  interpret anon_papp_profile n_voters parties committee_size A
-    by fact
-  show ?thesis
-    using A_nonempty A_subset size_A
-    by unfold_locales
-       (auto simp: lift_profile_def size_mset_sum_mset image_mset.compositionality o_def)
-qed
-
-sublocale lowered: anon_papp n_voters parties committee_size "r \<circ> lift_profile"
-proof
-  fix A assume "lowered.is_pref_profile A"
-  hence "is_pref_profile (lift_profile A)"
-    by blast
-  hence "is_committee (r (lift_profile A))"
-    using rule_wf by blast
-  thus "lowered.is_committee ((r \<circ> lift_profile) A)"
-    by simp
-qed
-
-sublocale lowered: weak_rep_anon_papp n_voters parties committee_size "r \<circ> lift_profile"
-proof
-  fix A x
-  assume A: "lowered.is_pref_profile A" and x: "n_voters \<le> committee_size * count A {x}"
-  from A have A': "is_pref_profile (lift_profile A)"
-    by blast
-  from x have "l * n_voters \<le> l * (committee_size * count A {x})"
-    by (rule mult_left_mono) auto
-  also have "\<dots> = committee_size * count (lift_profile A) {x}"
-    by simp
-  finally have "x \<in># r (lift_profile A)"
-    by (intro weak_representation A')
-  thus "x \<in># (r \<circ> lift_profile) A"
-    by simp
-qed
-
-sublocale lowered: card_stratproof_anon_papp n_voters parties committee_size "r \<circ> lift_profile"
-proof
-  fix A X Y
-  show "\<not>lowered.card_manipulable A X Y"
-    unfolding lowered.card_manipulable_def
-  proof (rule notI, elim conjE)
-    assume A: "lowered.is_pref_profile A" and XY: "X \<in># A" "Y \<noteq> {}" "Y \<subseteq> parties"
-    assume *: "(r \<circ> lift_profile) A \<prec>[lowered.committee_preference X] 
-               (r \<circ> lift_profile) (A - {#X#} + {#Y#})"
-    interpret anon_papp_profile n_voters parties committee_size A
-      by fact
-    have X: "X \<noteq> {}" "X \<subseteq> parties"
-      using XY A_nonempty A_subset by auto
-
-    define A' where "A' = A - {#X#}"
-    have A': "A = A' + {#X#}"
-      using XY by (simp add: A'_def)
-
-    have "r (lift_profile A) \<prec>[committee_preference X]
-          r (lift_profile (A - {#X#} + {#Y#}))"
-      using * by simp
-    also have "r (lift_profile (A - {#X#} + {#Y#})) \<preceq>[committee_preference X]
-               r (lift_profile A - {#X#} + {#Y#})"
-    proof -
-      have "r (replicate_mset (l - 1) Y + (lift_profile A' + {#Y#})) \<preceq>[committee_preference X]
-            r (replicate_mset (l - 1) X + (lift_profile A' + {#Y#}))"
-      proof (rule proposition2)
-        show "size (lift_profile A' + {#Y#}) + (l - 1) = l * n_voters"
-          using XY l_pos n_voters_pos
-          by (simp add: A'_def size_lift_profile size_Diff_singleton 
-                        algebra_simps Suc_diff_le size_A)
-      next
-        show "{} \<notin># lift_profile A' + {#Y#} + replicate_mset (l - 1) Y"
-          using XY A_nonempty by (auto simp: A'_def dest: in_diffD)
-      next
-        show "\<forall>X'\<in>#lift_profile A' + {#Y#} + replicate_mset (l - 1) Y. X' \<subseteq> parties"
-          using XY A_subset by (auto simp: A'_def dest: in_diffD)
-      qed (use X in auto)
-      thus ?thesis
-        by (simp add: A' replicate_mset_rec l_pos lift_profile_def)
-    qed
-    finally have "card_manipulable (lift_profile A) X Y"
-      unfolding card_manipulable_def using XY A by auto
-    with not_manipulable show False
-      by blast
-  qed
-qed
-
-sublocale lowered: card_stratproof_weak_rep_anon_papp n_voters parties committee_size "r \<circ> lift_profile"
-  ..
-
-end
-
-
-locale divide_voters_card_stratproof_weak_prop_rep_anon_papp =
-  card_stratproof_weak_prop_rep_anon_papp "l * n_voters" parties committee_size r
-  for l n_voters parties committee_size r
-begin
-
-sublocale divide_voters_card_stratproof_weak_rep_anon_papp ..
-
-sublocale lowered: card_stratproof_weak_prop_rep_anon_papp
-  n_voters parties committee_size "r \<circ> lift_profile"
-proof
-  fix A x l'
-  assume A: "lowered.is_pref_profile A" and x: "l' * n_voters \<le> committee_size * count A {x}"
-  from A have A': "is_pref_profile (lift_profile A)"
-    by blast
-  from x have "l * (l' * n_voters) \<le> l * (committee_size * count A {x})"
-    by (rule mult_left_mono) auto
-  also have "\<dots> = committee_size * count (lift_profile A) {x}"
-    by simp
-  also have "l * (l' * n_voters) = l' * (l * n_voters)"
-    by (simp add: algebra_simps)
-  finally have "count (r (lift_profile A)) x \<ge> l'"
-    by (intro weak_proportional_representation A')
-  thus "count ((r \<circ> lift_profile) A) x \<ge> l'"
-    by simp
-qed
-
-end
-
-
-
-subsection \<open>Decreasing the number of parties\<close>
-
-text \<open>
-  If we have a PAPP rule that satisfies weak representation and cardinality strategyproofness,
-  for $m$ parties, we can turn it into one for $m-1$ parties. This is done by simply
-  duplicating one particular party (say \<open>x\<close>) in the preference profile, i.e.\ whenever
-  \<open>x\<close> is part of an approval list, we add a clone of \<open>x\<close> (say \<open>y\<close>) as well. Should \<open>y\<close> then end up
-  in the committee, we simply replace it with \<open>x\<close>.
-
-  Consequently, if we have an impossibility result for $k$ parties, it also holds for
-  $\geq m$ parties.
-\<close>
-locale remove_alt_card_stratproof_weak_rep_anon_papp =
-  card_stratproof_weak_rep_anon_papp n_voters parties committee_size r
-  for n_voters and parties :: "'a set" and committee_size r +
-  fixes x y :: 'a
-  assumes xy: "x \<in> parties" "y \<in> parties" "x \<noteq> y"
-begin
-
-definition lift_applist :: "'a set \<Rightarrow> 'a set" where
-  "lift_applist X = (if x \<in> X then insert y X else X)"
-
-definition lift_profile :: "'a set multiset \<Rightarrow> 'a set multiset" where
-  "lift_profile A = image_mset lift_applist A"
-
-definition lower_result where "lower_result C = image_mset (\<lambda>z. if z = y then x else z) C"
-
-definition lowered where "lowered = lower_result \<circ> r \<circ> lift_profile"
-
-
-lemma lift_profile_empty [simp]: "lift_profile {#} = {#}"
-  by (simp add: lift_profile_def)
-
-lemma lift_profile_add_mset [simp]:
-  "lift_profile (add_mset X A) = add_mset (lift_applist X) (lift_profile A)"
-  by (simp add: lift_profile_def)
-
-lemma empty_in_lift_profile_iff [simp]: "{} \<in># lift_profile A \<longleftrightarrow> {} \<in># A"
-  by (auto simp: lift_applist_def lift_profile_def)
-
-lemma size_lift_profile [simp]: "size (lift_profile A) = size A"
-  by (simp add: lift_profile_def)
-
-lemma lift_applist_eq_self_iff [simp]: "lift_applist X = X \<longleftrightarrow> x \<notin> X \<or> y \<in> X"
-  by (auto simp: lift_applist_def)
-
-lemma lift_applist_eq_self_iff' [simp]: "lift_applist (X - {y}) = X \<longleftrightarrow> (x \<in> X \<longleftrightarrow> y \<in> X)"
-  by (cases "y \<in> X") (auto simp: lift_applist_def xy)
-
-lemma in_lift_applist_iff: "z \<in> lift_applist X \<longleftrightarrow> z \<in> X \<or> (z = y \<and> x \<in> X)"
-  by (auto simp: lift_applist_def)
-
-lemma count_lift_profile:
-  assumes "\<forall>Y\<in>#A. y \<notin> Y"
-  shows   "count (lift_profile A) X = (if x \<in> X \<longleftrightarrow> y \<in> X then count A (X - {y}) else 0)"
-  using assms xy by (induction A) (auto simp: lift_applist_def)
-
-lemma y_notin_lower_result [simp]: "y \<notin># lower_result C"
-  using xy by (auto simp: lower_result_def)
-
-lemma lower_result_subset: "set_mset (lower_result C) \<subseteq> insert x (set_mset C - {y})"
-  using xy by (auto simp: lower_result_def)
-
-lemma lower_result_subset': "set_mset C \<subseteq> parties \<Longrightarrow> set_mset (lower_result C) \<subseteq> parties"
-  using xy by (auto simp: lower_result_def)
-
-lemma size_lower_result [simp]: "size (lower_result C) = size C"
-  by (simp add: lower_result_def)
-
-lemma count_lower_result:
-  "count (lower_result C) z =
-     (if z = y then 0
-      else if z = x then count C x + count C y
-      else count C z)"
-  using xy by (induction C) (auto simp: lower_result_def)
-
-lemma in_lower_result_iff:
-  "z \<in># lower_result C \<longleftrightarrow> z \<noteq> y \<and> (z \<in># C \<or> (z = x \<and> y \<in># C))"
-  unfolding lower_result_def using xy by (induction C) auto
-
-
-sublocale lowered: anon_papp_election n_voters "parties - {y}"
-  by standard (use n_voters_pos xy in auto)
-
-lemma is_pref_profile_lift_profile [intro]:
-  assumes "lowered.is_pref_profile A"
-  shows   "is_pref_profile (lift_profile A)"
-proof -
-  interpret anon_papp_profile n_voters "parties - {y}" committee_size A
-    by fact
-  show ?thesis
-    using A_nonempty A_subset size_A
-    by unfold_locales
-       (auto simp: lift_profile_def lift_applist_def xy 
-                   size_mset_sum_mset image_mset.compositionality o_def)
-qed
-
-sublocale lowered: anon_papp n_voters "parties - {y}" committee_size lowered
-proof
-  fix A assume "lowered.is_pref_profile A"
-  hence "is_pref_profile (lift_profile A)"
-    by blast
-  hence "is_committee (r (lift_profile A))"
-    using rule_wf by blast
-  thus "lowered.is_committee (lowered A)"
-    unfolding lowered.is_committee_def is_committee_def lowered_def
-    using lower_result_subset'[of "r (lift_profile A)"] by auto
-qed
-
-sublocale lowered: weak_rep_anon_papp n_voters "parties - {y}" committee_size lowered
-proof
-  fix A z
-  assume A: "lowered.is_pref_profile A" and z: "n_voters \<le> committee_size * count A {z}"
-  interpret A: anon_papp_profile n_voters "parties - {y}" committee_size A
-    by fact
-  have "committee_size > 0"
-    using z n_voters_pos by (intro Nat.gr0I) auto
-
-  from A have A': "is_pref_profile (lift_profile A)"
-    by blast
-  have "count A {z} > 0"
-    using z n_voters_pos by (intro Nat.gr0I) auto
-  hence "{z} \<in># A"
-    by simp
-  hence z': "z \<in> parties - {y}"
-    using A.A_subset z by auto
-
-  define C where "C = r (lift_profile A)"
-
-  show "z \<in># lowered A"
-  proof (cases "z = x")
-    case False
-    have "n_voters \<le> committee_size * count A {z}"
-      by fact
-    also have "count A {z} \<le> count (lift_profile A) {z}"
-      using A.A_subset z' False by (subst count_lift_profile) auto
-    hence "committee_size * count A {z} \<le> committee_size * count (lift_profile A) {z}"
-      by (intro mult_left_mono) auto
-    finally have "z \<in># r (lift_profile A)"
-      by (intro weak_representation A')
-    thus "z \<in># lowered A"
-      using False z' by (simp add: lowered_def in_lower_result_iff)
-  next
-    case [simp]: True
-    have "1 \<le> size {#z \<in># C. z \<in> {x, y}#}"
-      unfolding C_def
-    proof (rule proposition3)
-      have [simp]: "{x, y} - {y} = {x}"
-        using xy by auto
-      hence "n_voters \<le> committee_size * count (lift_profile A) {x, y}"
-        using xy A.A_subset z by (subst count_lift_profile) auto
-      thus "int 1 * \<lceil>real n_voters / real committee_size\<rceil> \<le> int (count (lift_profile A) {x, y})"
-        using \<open>committee_size > 0\<close>
-        by (auto simp: ceiling_le_iff field_simps simp flip: of_nat_mult)
-    qed (use A' xy \<open>committee_size > 0\<close> in auto)
-    also have "\<dots> = count C x + count C y"
-      using xy by (induction C) auto
-    also have "\<dots> = count (lowered A) x"
-      using xy by (simp add: lowered_def count_lower_result C_def)
-    finally show "z \<in># lowered A"
-      by simp
-  qed
-qed
-
-lemma filter_lower_result_eq:
-  "y \<notin> X \<Longrightarrow> {#x \<in># lower_result C. x \<in> X#} = lower_result {#x \<in># C. x \<in> lift_applist X#}"
-  by (induction C) (auto simp: lower_result_def lift_applist_def)
-
-sublocale lowered: card_stratproof_anon_papp n_voters "parties - {y}" committee_size lowered
-proof
-  fix A X Y
-  show "\<not>lowered.card_manipulable A X Y"
-    unfolding lowered.card_manipulable_def
-  proof (rule notI, elim conjE)
-    assume A: "lowered.is_pref_profile A" and XY: "X \<in># A" "Y \<noteq> {}" "Y \<subseteq> parties - {y}"
-    assume *: "lowered A \<prec>[lowered.committee_preference X] lowered (A - {#X#} + {#Y#})"
-    interpret anon_papp_profile n_voters "parties - {y}" committee_size A
-      by fact
-    have X: "X \<noteq> {}" "X \<subseteq> parties - {y}"
-      using XY A_nonempty A_subset by auto
-    define A' where "A' = A - {#X#}"
-    have A': "A = A' + {#X#}"
-      using XY by (simp add: A'_def)
-
-    from * have "size {#x \<in># lower_result (r (lift_profile A' + {#lift_applist X#})). x \<in> X#} <
-                 size {#x \<in># lower_result (r (lift_profile A' + {#lift_applist Y#})). x \<in> X#}"
-      by (simp add: lowered_def A' lowered.strong_committee_preference_iff)
-    also have "{#x \<in># lower_result (r (lift_profile A' + {#lift_applist X#})). x \<in> X#} =
-               lower_result {#x \<in># r (lift_profile A' + {#lift_applist X#}). x \<in> lift_applist X#}"
-      using X by (subst filter_lower_result_eq) auto
-    also have "{#x \<in># lower_result (r (lift_profile A' + {#lift_applist Y#})). x \<in> X#} =
-               lower_result {#x \<in># r (lift_profile A' + {#lift_applist Y#}). x \<in> lift_applist X#}"
-      using X by (subst filter_lower_result_eq) auto
-    finally have "size {#x \<in># r (lift_profile A' + {#lift_applist X#}). x \<in> lift_applist X#} <
-                  size {#x \<in># r (lift_profile A' + {#lift_applist Y#}). x \<in> lift_applist X#}"
-      by simp
-    hence "r (lift_profile A' + {#lift_applist X#}) \<prec>[committee_preference (lift_applist X)]
-           r (lift_profile A' + {#lift_applist Y#})"
-      by (simp add: strong_committee_preference_iff)
-    moreover have "\<not>r (lift_profile A' + {#lift_applist X#}) \<prec>[committee_preference (lift_applist X)]
-                    r (lift_profile A' + {#lift_applist Y#})"
-    proof (rule not_manipulable' [where Y = "lift_applist Y"])
-      have "is_pref_profile (lift_profile A)"
-        using A by blast
-      thus "is_pref_profile (lift_profile A' + {#lift_applist X#})"
-        using A by (simp add: A')
-    next
-      have "is_pref_profile (lift_profile (A - {#X#} + {#Y#}))"
-        using A  XY lowered.is_pref_profile_replace by blast
-      thus "is_pref_profile (lift_profile A' + {#lift_applist Y#})"
-        by (simp add: A')
-    qed auto
-    ultimately show False
-      by contradiction
-  qed
-qed
-
-sublocale lowered: card_stratproof_weak_rep_anon_papp n_voters "parties - {y}" committee_size lowered
-  ..
-
-end
-
-
-text \<open>
-  The following lemma is now simply an iterated application of the above. This allows us to
-  restrict a P-APP rule to any non-empty subset of parties.
-\<close>
-lemma card_stratproof_weak_rep_anon_papp_restrict_parties:
-  assumes "card_stratproof_weak_rep_anon_papp n parties k r" "parties' \<subseteq> parties" "parties' \<noteq> {}"
-  shows   "\<exists>r. card_stratproof_weak_rep_anon_papp n parties' k r"
-proof -
-  have "finite parties"
-  proof -
-    interpret card_stratproof_weak_rep_anon_papp n parties k r
-      by fact
-    show ?thesis
-      by (rule finite_parties)
-  qed
-  thus ?thesis
-    using assms
-  proof (induction parties arbitrary: r rule: finite_psubset_induct)
-    case (psubset parties r)
-    show ?thesis
-    proof (cases "parties = parties'")
-      case True
-      thus ?thesis
-        using psubset.prems by auto
-    next
-      case False
-      obtain x where x: "x \<in> parties'"
-        using psubset.prems by blast
-      from False and psubset.prems have "parties - parties' \<noteq> {}"
-        by auto
-      then obtain y where y: "y \<in> parties - parties'"
-        by blast
-
-      interpret card_stratproof_weak_rep_anon_papp n parties k r
-        by fact
-      interpret remove_alt_card_stratproof_weak_rep_anon_papp n parties k r x y
-        by standard (use x y psubset.prems in auto)
-      show ?thesis
-      proof (rule psubset.IH)
-        show "parties - {y} \<subset> parties" and "parties' \<subseteq> parties - {y}" "parties' \<noteq> {}"
-          using x y psubset.prems by auto
-      next
-        show "card_stratproof_weak_rep_anon_papp n (parties - {y}) k lowered"
-          using lowered.card_stratproof_weak_rep_anon_papp_axioms .
-      qed
-    qed
-  qed
-qed
-
-
-
-subsection \<open>Decreasing the committee size\<close>
-
-text \<open>
-  If we have a PAPP rule that satisfies weak representation and cardinality strategyproofness,
-  for $l(k+1)$ voters, $m+1$ parties, and a committee size of $k+1$, we can turn it into
-  one for $lk$ voters, $m$ parties, and a committee size of $k$.
-
-  This is done by again cloning a party \<open>x\<close> into a new party \<open>y\<close> and additionally
-  adding \<open>l\<close> new voters whose preferences are \<open>{x, y}\<close>. We again replace any \<open>y\<close> occuring in the
-  output committee with \<open>x\<close>. Weak representation then ensures that \<open>x\<close> occurs in the output
-  at least once, and we then simply remove one \<open>x\<close> from the committee to obtain an output
-  committee of size \<open>k - 1\<close>.
-
-  Consequently, if we have an impossibility result for a committee size of $m$, we can
-  extend it to a larger committee size, but at the cost of introducing a new party
-  and new voters, and with a restriction on the number of voters.
-\<close>
-(* n / k = l *)
-locale decrease_committee_card_stratproof_weak_rep_anon_papp =
-  card_stratproof_weak_rep_anon_papp "l * (k + 1)" "insert y parties" "k + 1" r
-  for l k y and parties :: "'a set" and r +
-  fixes x :: 'a
-  assumes xy: "x \<in> parties" "y \<notin> parties"
-  assumes k: "k > 0"
-begin
-
-definition lift_applist :: "'a set \<Rightarrow> 'a set" where
-  "lift_applist X = (if x \<in> X then insert y X else X)"
-
-definition lift_profile :: "'a set multiset \<Rightarrow> 'a set multiset" where
-  "lift_profile A = image_mset lift_applist A + replicate_mset l {x, y}"
-
-definition lower_result
-  where "lower_result C = image_mset (\<lambda>z. if z = y then x else z) C - {#x#}"
-
-definition lowered where "lowered = lower_result \<circ> r \<circ> lift_profile"
-
-
-lemma l: "l > 0"
-  using n_voters_pos by auto
-
-lemma x_neq_y [simp]: "x \<noteq> y" "y \<noteq> x"
-  using xy by auto
-
-lemma lift_profile_empty [simp]: "lift_profile {#} = replicate_mset l {x, y}"
-  by (simp add: lift_profile_def)
-
-lemma lift_profile_add_mset [simp]:
-  "lift_profile (add_mset X A) = add_mset (lift_applist X) (lift_profile A)"
-  by (simp add: lift_profile_def)
-
-lemma empty_in_lift_profile_iff [simp]: "{} \<in># lift_profile A \<longleftrightarrow> {} \<in># A"
-  by (auto simp: lift_applist_def lift_profile_def)
-
-lemma size_lift_profile [simp]: "size (lift_profile A) = size A + l"
-  by (simp add: lift_profile_def)
-
-lemma lift_applist_eq_self_iff [simp]: "lift_applist X = X \<longleftrightarrow> x \<notin> X \<or> y \<in> X"
-  by (auto simp: lift_applist_def)
-
-lemma lift_applist_eq_self_iff' [simp]: "lift_applist (X - {y}) = X \<longleftrightarrow> (x \<in> X \<longleftrightarrow> y \<in> X)"
-  by (cases "y \<in> X") (auto simp: lift_applist_def xy)
-
-lemma in_lift_applist_iff: "z \<in> lift_applist X \<longleftrightarrow> z \<in> X \<or> (z = y \<and> x \<in> X)"
-  by (auto simp: lift_applist_def)
-
-lemma count_lift_profile:
-  assumes "\<forall>Y\<in>#A. y \<notin> Y"
-  shows   "count (lift_profile A) X =
-             (if x \<in> X \<longleftrightarrow> y \<in> X then count A (X - {y}) else 0) +
-             (if X = {x, y} then l else 0)"
-  using assms xy by (induction A) (auto simp: lift_applist_def)
-
-
-
-lemma y_notin_lower_result [simp]: "y \<notin># lower_result C"
-  using xy by (auto simp: lower_result_def dest: in_diffD)
-
-lemma lower_result_subset: "set_mset (lower_result C) \<subseteq> insert x (set_mset C - {y})"
-  using xy by (auto simp: lower_result_def dest: in_diffD)
-
-lemma lower_result_subset': "set_mset C \<subseteq> insert y parties \<Longrightarrow> set_mset (lower_result C) \<subseteq> parties"
-  by (rule order.trans[OF lower_result_subset]) (use xy in auto)
-
-lemma size_lower_result [simp]:
-  assumes "x \<in># C \<or> y \<in># C"
-  shows   "size (lower_result C) = size C - 1"
-  using assms by (auto simp: lower_result_def size_Diff_singleton)
-
-lemma size_lower_result': "size (lower_result C) = size C - (if x \<in># C \<or> y \<in># C then 1 else 0)"
-proof -
-  define f where "f = (\<lambda>C. image_mset (\<lambda>z. if z = y then x else z) C)"
-  have "size (lower_result C) = size (f C - {#x#})"
-    by (simp add: lower_result_def f_def)
-  also have "\<dots> = size (f C) - (if x \<in># f C then 1 else 0)"
-    by (simp add: diff_single_trivial size_Diff_singleton)
-  finally show ?thesis
-    by (auto simp: f_def)
-qed
-
-lemma count_lower_result:
-  "count (lower_result C) z =
-     (if z = y then 0
-      else if z = x then count C x + count C y - 1
-      else count C z)" (is "_ = ?rhs")
-proof -
-  define f where "f = (\<lambda>C. image_mset (\<lambda>z. if z = y then x else z) C)"
-  have "count (lower_result C) z = count (f C - {#x#}) z"
-    by (simp add: lower_result_def f_def)
-  also have "\<dots> = count (f C) z - (if z = x then 1 else 0)"
-    by auto
-  also have "count (f C) z = (if z = y then 0 else if z = x then count C x + count C y else count C z)"
-    using xy by (induction C)  (auto simp: f_def)
-  also have "\<dots> - (if z = x then 1 else 0) = ?rhs"
-    by auto
-  finally show ?thesis .
-qed
-
-lemma in_lower_resultD:
-  "z \<in># lower_result C \<Longrightarrow> z = x \<or> z \<in># C"
-  using xy by (auto simp: lower_result_def dest!: in_diffD)
-
-lemma in_lower_result_iff:
-  "z \<in># lower_result C \<longleftrightarrow> z \<noteq> y \<and> (if z = x then count C x + count C y > 1 else z \<in># C)"
-  (is "_ = ?rhs")
-proof -
-  have "z \<in># lower_result C \<longleftrightarrow> count (lower_result C) z > 0"
-    by auto
-  also have "\<dots> \<longleftrightarrow> ?rhs"
-    by (subst count_lower_result) auto
-  finally show ?thesis .
-qed
-
-lemma filter_lower_result_eq:
-  assumes "y \<notin> X"
-  shows   "{#z \<in># lower_result C. z \<in> X#} = lower_result {#z \<in># C. z \<in> lift_applist X#}"
-proof -
-  define f where "f = (\<lambda>C. {#if z = y then x else z. z \<in># C#})"
-  have "lower_result {#z \<in># C. z \<in> lift_applist X#} = f {#z \<in># C. z \<in> lift_applist X#} - {#x#}"
-    by (simp add: f_def lower_result_def)
-  also have "f {#z \<in># C. z \<in> lift_applist X#} = {#z \<in># f C. z \<in> X#}"
-    using assms by (induction C) (auto simp: f_def lift_applist_def)
-  also have "\<dots> - {#x#} = {#z \<in># f C - {#x#}. z \<in> X#}"
-    by (subst filter_diff_mset') auto
-  also have "f C - {#x#} = lower_result C"
-    by (simp add: f_def lower_result_def)
-  finally show ?thesis ..
-qed
-
-
-sublocale lowered: anon_papp_election "l * k" parties k
-  by standard (use n_voters_pos xy finite_parties k in auto)
-
-lemma is_pref_profile_lift_profile [intro]:
-  assumes "lowered.is_pref_profile A"
-  shows   "is_pref_profile (lift_profile A)"
-proof -
-  interpret A: anon_papp_profile "l * k" parties k A
-    by fact
-  show ?thesis
-    using A.A_nonempty A.A_subset A.size_A l
-    by unfold_locales
-       (auto simp: lift_profile_def lift_applist_def xy 
-                   size_mset_sum_mset image_mset.compositionality o_def)
-qed
-
-lemma is_committee_lower_result:
-  assumes "is_committee C" "x \<in># C \<or> y \<in># C"
-  shows   "lowered.is_committee (lower_result C)"
-  using assms unfolding is_committee_def lowered.is_committee_def
-  using lower_result_subset'[of C] by auto
-
-lemma x_or_y_in_r_lift_profile:
-  assumes "lowered.is_pref_profile A"
-  shows   "x \<in># r (lift_profile A) \<or> y \<in># r (lift_profile A)"
-proof -
-  interpret A: anon_papp_profile "l * k" parties k A
-    by fact
-  have "size {#z \<in># r (lift_profile A). z \<in> {x, y}#} \<ge> 1"
-  proof (rule proposition3)
-    have "real (l * (k + 1)) / real (k + 1) = real l"
-      by (simp add: field_simps)
-    also have "int 1 * \<lceil>\<dots>\<rceil> = int l"
-      by simp
-    also have "l \<le> count (lift_profile A) {x, y}"
-      using xy A.A_subset by (subst count_lift_profile) auto
-    finally show "int 1 * \<lceil>real (l * (k + 1)) / real (k + 1)\<rceil> \<le> int (count (lift_profile A) {x, y})"
-      by simp
-  next
-    show "is_pref_profile (lift_profile A)"
-      by (intro is_pref_profile_lift_profile) fact
-  qed (use xy in auto)
-  hence "{#z \<in># r (lift_profile A). z \<in> {x, y}#} \<noteq> {#}"
-    by force
-  thus ?thesis
-    by auto
-qed
-
-sublocale lowered: anon_papp "l * k" parties k lowered
-proof
-  fix A assume A: "lowered.is_pref_profile A"
-  hence "is_pref_profile (lift_profile A)"
-    by blast
-  hence "is_committee (r (lift_profile A))"
-    using rule_wf by blast
-  thus "lowered.is_committee (lowered A)"
-    unfolding lowered_def o_def using x_or_y_in_r_lift_profile[of A] A
-    by (intro is_committee_lower_result) auto
-qed
-
-sublocale lowered: weak_rep_anon_papp "l * k" parties k lowered
-proof
-  fix A z
-  assume A: "lowered.is_pref_profile A" and z: "l * k \<le> k * count A {z}"
-  interpret A: anon_papp_profile "l * k" "parties" k A
-    by fact
-
-  from A have A': "is_pref_profile (lift_profile A)"
-    by blast
-  have "count A {z} > 0"
-    using z k n_voters_pos by (intro Nat.gr0I) auto
-  hence "{z} \<in># A"
-    by simp
-  hence z': "z \<in> parties"
-    using A.A_subset z by auto
-  hence [simp]: "y \<noteq> z" "z \<noteq> y"
-    using xy by auto
-
-  define C where "C = r (lift_profile A)"
-
-  show "z \<in># lowered A"
-  proof (cases "z = x")
-    case False
-    have "l \<le> count A {z}"
-      using z k by (simp add: algebra_simps)
-    hence "l * (k + 1) \<le> (k + 1) * count A {z}"
-      by (subst mult.commute, intro mult_right_mono) auto
-    also have "count A {z} = count (lift_profile A) {z}"
-      using False A.A_subset xy by (subst count_lift_profile) auto
-    finally have "z \<in># r (lift_profile A)"
-      by (intro weak_representation A')
-    thus "z \<in># lowered A"
-      using False by (auto simp: lowered_def in_lower_result_iff)
-  next
-    case [simp]: True
-    from xy have [simp]: "{x, y} - {y} = {x}"
-      by auto
-
-    have "size {#z \<in># C. z \<in> {x, y}#} \<ge> 2"
-      unfolding C_def
-    proof (rule proposition3)
-      have "real (l * (k + 1)) / real (k + 1) = l"
-        unfolding of_nat_mult using k by (simp add: divide_simps)
-      also have "int 2 * \<lceil>\<dots>\<rceil> = int (2 * l)"
-        by simp
-      also have "\<dots> \<le> count (lift_profile A) {x, y}"
-        using z k xy A.A_subset by (subst count_lift_profile) auto
-      finally show "int 2 * \<lceil>real (l * (k + 1)) / real (k + 1)\<rceil> \<le> \<dots>" .
-    qed (use A' xy in auto)
-    also have "size {#z \<in># C. z \<in> {x, y}#} = count C x + count C y"
-      by (induction C) auto
-    finally have "x \<in># lower_result C"
-      by (subst in_lower_result_iff) auto
-    thus "z \<in># lowered A"
-      by (simp add: lowered_def C_def)
-  qed
-qed
-
-sublocale lowered: card_stratproof_anon_papp "l * k" parties k lowered
-proof
-  fix A X Y
-  show "\<not>lowered.card_manipulable A X Y"
-    unfolding lowered.card_manipulable_def
-  proof (rule notI, elim conjE)
-    assume A: "lowered.is_pref_profile A" and XY: "X \<in># A" "Y \<noteq> {}" "Y \<subseteq> parties"
-    assume *: "lowered A \<prec>[lowered.committee_preference X] lowered (A - {#X#} + {#Y#})"
-    interpret anon_papp_profile "l * k" "parties" k A
-      by fact
-    have X: "X \<noteq> {}" "X \<subseteq> parties"
-      using XY A_nonempty A_subset by auto
-    define A' where "A' = A - {#X#}"
-    have A': "A = A' + {#X#}"
-      using XY by (simp add: A'_def)
-    from xy X XY have [simp]: "y \<notin> X" "y \<notin> Y"
-      by auto
-
-    define Al1 where "Al1 = lift_profile A"
-    define Al2 where "Al2 = lift_profile (A' + {#Y#})"
-    have A'_plus_Y: "lowered.is_pref_profile (A' + {#Y#})"
-      unfolding A'_def using A XY lowered.is_pref_profile_replace by blast
-    have Al1: "is_pref_profile Al1"
-      unfolding Al1_def using A by blast
-    have Al2: "is_pref_profile Al2"
-      unfolding Al2_def unfolding A'_def using A XY lowered.is_pref_profile_replace by blast
-
-    have size_aux: "size (lower_result {#x \<in># r (lift_profile A). x \<in> lift_applist X#}) =
-                    size {#x \<in># r (lift_profile A). x \<in> lift_applist X#} - (if x \<in> X then 1 else 0)"
-      if A: "lowered.is_pref_profile A" for A
-      using x_or_y_in_r_lift_profile[OF A] 
-      by (subst size_lower_result') (auto simp: lift_applist_def)
-
-    from * have "size {#x \<in># lower_result (r Al1). x \<in> X#} <
-                 size {#x \<in># lower_result (r Al2). x \<in> X#}"
-      by (simp add: Al1_def Al2_def lowered_def A' lowered.strong_committee_preference_iff)
-    also have "{#x \<in># lower_result (r Al1). x \<in> X#} = lower_result {#x \<in># r Al1. x \<in> lift_applist X#}"
-      using X xy by (subst filter_lower_result_eq) auto
-    also have "{#x \<in># lower_result (r Al2). x \<in> X#} = lower_result {#x \<in># r Al2. x \<in> lift_applist X#}"
-      using X xy by (subst filter_lower_result_eq) auto
-    also have "size (lower_result {#x \<in># r Al1. x \<in> lift_applist X#}) =
-               size {#x \<in># r Al1. x \<in> lift_applist X#} - (if x \<in> X then 1 else 0)"
-      unfolding Al1_def by (rule size_aux) fact
-    also have "size (lower_result {#x \<in># r Al2. x \<in> lift_applist X#}) =
-               size {#x \<in># r Al2. x \<in> lift_applist X#} - (if x \<in> X then 1 else 0)"
-      unfolding Al2_def by (rule size_aux) fact
-    finally have "size {#x \<in># r Al1. x \<in> lift_applist X#} < size {#x \<in># r Al2. x \<in> lift_applist X#}"
-      by auto
-    hence "r Al1 \<prec>[committee_preference (lift_applist X)] r Al2"
-      by (simp add: strong_committee_preference_iff)
-
-    moreover have "\<not>r Al1 \<prec>[committee_preference (lift_applist X)] r Al2"
-      by (rule not_manipulable' [where Y = "lift_applist Y"])
-         (use Al1 Al2 in \<open>auto simp: Al1_def Al2_def A'\<close>)
-
-    ultimately show False
-      by contradiction
-  qed
-qed
-
-sublocale lowered: card_stratproof_weak_rep_anon_papp "l * k" parties k lowered
-  ..
-
-end
-
-
-text \<open>
-  For Weak \<^emph>\<open>Proportional\<close> Representation, the lowering argument to decrease the committee size
-  is somewhat easier since it does not involve adding a new party; instead, we simply
-  add \<open>l\<close> new voters whose preferences are \<open>{x}\<close>.
-\<close>
-locale decrease_committee_card_stratproof_weak_prop_rep_anon_papp =
-  card_stratproof_weak_prop_rep_anon_papp "l * (k + 1)" parties "k + 1" r
-  for l k and parties :: "'a set" and r +
-  fixes x :: 'a
-  assumes x: "x \<in> parties"
-  assumes k: "k > 0"
-begin
-
-definition lift_profile :: "'a set multiset \<Rightarrow> 'a set multiset" where
-  "lift_profile A = A + replicate_mset l {x}"
-
-definition lower_result
-  where "lower_result C = C - {#x#}"
-
-definition lowered where "lowered = lower_result \<circ> r \<circ> lift_profile"
-
-
-lemma l: "l > 0"
-  using n_voters_pos by auto
-
-lemma lift_profile_empty [simp]: "lift_profile {#} = replicate_mset l {x}"
-  by (simp add: lift_profile_def)
-
-lemma lift_profile_add_mset [simp]:
-  "lift_profile (add_mset X A) = add_mset X (lift_profile A)"
-  by (simp add: lift_profile_def)
-
-lemma empty_in_lift_profile_iff [simp]: "{} \<in># lift_profile A \<longleftrightarrow> {} \<in># A"
-  by (auto simp: lift_profile_def)
-
-lemma size_lift_profile [simp]: "size (lift_profile A) = size A + l"
-  by (simp add: lift_profile_def)
-
-lemma count_lift_profile:
-  "count (lift_profile A) X = count A X + (if X = {x} then l else 0)"
-  by (auto simp: lift_profile_def)
-
-
-lemma size_lower_result [simp]:
-  assumes "x \<in># C"
-  shows   "size (lower_result C) = size C - 1"
-  using assms by (auto simp: lower_result_def size_Diff_singleton)
-
-lemma size_lower_result': "size (lower_result C) = size C - (if x \<in># C then 1 else 0)"
-  by (induction C) (auto simp: lower_result_def size_Diff_singleton)
-
-lemma count_lower_result:
-  "count (lower_result C) z = count C z - (if z = x then 1 else 0)"
-  by (auto simp: lower_result_def)
-
-lemma in_lower_resultD:
-  "z \<in># lower_result C \<Longrightarrow> z \<in># C"
-  by (auto simp: lower_result_def dest!: in_diffD)
-
-lemma in_lower_result_iff:
-  "z \<in># lower_result C \<longleftrightarrow> (if z = x then count C x > 1 else z \<in># C)"
-  (is "_ = ?rhs")
-proof -
-  have "z \<in># lower_result C \<longleftrightarrow> count (lower_result C) z > 0"
-    by auto
-  also have "\<dots> \<longleftrightarrow> ?rhs"
-    by (subst count_lower_result) auto
-  finally show ?thesis .
-qed
-
-
-sublocale lowered: anon_papp_election "l * k" parties k
-  by standard (use n_voters_pos finite_parties k in auto)
-
-lemma is_pref_profile_lift_profile [intro]:
-  assumes "lowered.is_pref_profile A"
-  shows   "is_pref_profile (lift_profile A)"
-proof -
-  interpret A: anon_papp_profile "l * k" parties k A
-    by fact
-  show ?thesis
-    using A.A_nonempty A.A_subset A.size_A l
-    by unfold_locales
-       (auto simp: lift_profile_def x size_mset_sum_mset image_mset.compositionality o_def)
-qed
-
-lemma is_committee_lower_result:
-  assumes "is_committee C" "x \<in># C"
-  shows   "lowered.is_committee (lower_result C)"
-  using assms unfolding is_committee_def lowered.is_committee_def
-  by (auto simp: lower_result_def size_Diff_singleton dest: in_diffD)
-
-lemma x_in_r_lift_profile:
-  assumes "lowered.is_pref_profile A"
-  shows   "x \<in># r (lift_profile A)"
-proof (rule weak_representation)
-  show "is_pref_profile (lift_profile A)"
-    using assms by blast
-next
-  have "(k + 1) * l \<le> (k + 1) * count (lift_profile A) {x}"
-    by (intro mult_left_mono) (auto simp: count_lift_profile)
-  thus "l * (k + 1) \<le> (k + 1) * count (lift_profile A) {x}"
-    by (simp add: algebra_simps)
-qed
-
-sublocale lowered: anon_papp "l * k" parties k lowered
-proof
-  fix A assume A: "lowered.is_pref_profile A"
-  hence "is_pref_profile (lift_profile A)"
-    by blast
-  hence "is_committee (r (lift_profile A))"
-    using rule_wf by blast
-  thus "lowered.is_committee (lowered A)"
-    unfolding lowered_def o_def using x_in_r_lift_profile[of A] A
-    by (intro is_committee_lower_result) auto
-qed
-
-sublocale lowered: weak_prop_rep_anon_papp "l * k" parties k lowered
-proof
-  fix A z l'
-  assume A: "lowered.is_pref_profile A" and z: "l' * (l * k) \<le> k * count A {z}"
-  interpret A: anon_papp_profile "l * k" "parties" k A
-    by fact
-
-  show "count (lowered A) z \<ge> l'"
-  proof (cases "l' > 0")
-    case False
-    thus ?thesis by auto
-  next
-    case l: True
-
-    from A have A': "is_pref_profile (lift_profile A)"
-      by blast
-    have "count A {z} > 0"
-      using z k n_voters_pos l by (intro Nat.gr0I) auto
-    hence "{z} \<in># A"
-      by simp
-    hence z': "z \<in> parties"
-      using A.A_subset z by auto
-  
-    define C where "C = r (lift_profile A)"
-  
-    show "count (lowered A) z \<ge> l'"
-    proof (cases "z = x")
-      case False
-      have "l' * l \<le> count A {z}"
-        using z k by (simp add: algebra_simps)
-      hence "l' * l * (k + 1) \<le> (k + 1) * count A {z}"
-        by (subst mult.commute, intro mult_right_mono) auto
-      also have "count A {z} = count (lift_profile A) {z}"
-        using False A.A_subset by (subst count_lift_profile) auto
-      finally have "count (r (lift_profile A)) z \<ge> l'"
-        by (intro weak_proportional_representation A') (auto simp: algebra_simps)
-      thus "l' \<le> count (lowered A) z"
-        using False by (simp add: lowered_def lower_result_def)
-    next
-      case [simp]: True
-      have "l' * l \<le> count A {x}"
-        using z k by (simp add: algebra_simps)
-      hence "l' * l * (k + 1) \<le> (k + 1) * count A {x}"
-        by (subst mult.commute, intro mult_right_mono) auto
-      also have "\<dots> + (k + 1) * l = (k + 1) * count (lift_profile A) {x}"
-        by (simp add: count_lift_profile algebra_simps)
-      finally have "(l' + 1) * (l * (k + 1)) \<le> (k + 1) * count (lift_profile A) {x}"
-        by (simp add: algebra_simps)
-      hence "count (r (lift_profile A)) x \<ge> l' + 1"
-        by (intro weak_proportional_representation A')
-      thus "l' \<le> count (lowered A) z"
-        by (simp add: lowered_def lower_result_def)
-    qed
-  qed
-qed
-
-sublocale lowered: card_stratproof_anon_papp "l * k" parties k lowered
-proof
-  fix A X Y
-  show "\<not>lowered.card_manipulable A X Y"
-    unfolding lowered.card_manipulable_def
-  proof (rule notI, elim conjE)
-    assume A: "lowered.is_pref_profile A" and XY: "X \<in># A" "Y \<noteq> {}" "Y \<subseteq> parties"
-    assume *: "lowered A \<prec>[lowered.committee_preference X] lowered (A - {#X#} + {#Y#})"
-    interpret anon_papp_profile "l * k" "parties" k A
-      by fact
-    have X: "X \<noteq> {}" "X \<subseteq> parties"
-      using XY A_nonempty A_subset by auto
-    define A' where "A' = A - {#X#}"
-    have A': "A = A' + {#X#}"
-      using XY by (simp add: A'_def)
-
-    define Al1 where "Al1 = lift_profile A"
-    define Al2 where "Al2 = lift_profile (A' + {#Y#})"
-    have A'_plus_Y: "lowered.is_pref_profile (A' + {#Y#})"
-      unfolding A'_def using A XY lowered.is_pref_profile_replace by blast
-    have Al1: "is_pref_profile Al1"
-      unfolding Al1_def using A by blast
-    have Al2: "is_pref_profile Al2"
-      unfolding Al2_def unfolding A'_def using A XY lowered.is_pref_profile_replace by blast
-
-    have size_aux: "size (lower_result {#x \<in># r (lift_profile A). x \<in> X#}) =
-                    size {#x \<in># r (lift_profile A). x \<in> X#} - (if x \<in> X then 1 else 0)"
-      if A: "lowered.is_pref_profile A" for A
-      using x_in_r_lift_profile[OF A]  by (subst size_lower_result') auto
-
-    from * have "size {#x \<in># lower_result (r Al1). x \<in> X#} <
-                 size {#x \<in># lower_result (r Al2). x \<in> X#}"
-      by (simp add: Al1_def Al2_def lowered_def A' lowered.strong_committee_preference_iff)
-    also have "{#x \<in># lower_result (r Al1). x \<in> X#} = lower_result {#x \<in># r Al1. x \<in> X#}"
-      using X x unfolding lower_result_def by (subst filter_diff_mset') auto
-    also have "{#x \<in># lower_result (r Al2). x \<in> X#} = lower_result {#x \<in># r Al2. x \<in> X#}"
-      using X x unfolding lower_result_def by (subst filter_diff_mset') auto
-    also have "size (lower_result {#x \<in># r Al1. x \<in> X#}) =
-               size {#x \<in># r Al1. x \<in> X#} - (if x \<in> X then 1 else 0)"
-      unfolding Al1_def by (rule size_aux) fact
-    also have "size (lower_result {#x \<in># r Al2. x \<in> X#}) =
-               size {#x \<in># r Al2. x \<in> X#} - (if x \<in> X then 1 else 0)"
-      unfolding Al2_def by (rule size_aux) fact
-    finally have "size {#x \<in># r Al1. x \<in> X#} < size {#x \<in># r Al2. x \<in> X#}"
-      by auto
-    hence "r Al1 \<prec>[committee_preference X] r Al2"
-      by (simp add: strong_committee_preference_iff)
-
-    moreover have "\<not>r Al1 \<prec>[committee_preference X] r Al2"
-      by (rule not_manipulable' [where Y = "Y"])
-         (use Al1 Al2 in \<open>auto simp: Al1_def Al2_def A'\<close>)
-
-    ultimately show False
-      by contradiction
-  qed
-qed
-
-sublocale lowered: card_stratproof_weak_prop_rep_anon_papp "l * k" parties k lowered
-  ..
-
-end
-
-end
diff --git a/thys/PAPP_Impossibility/#ROOT# b/thys/PAPP_Impossibility/#ROOT#
deleted file mode 100644
--- a/thys/PAPP_Impossibility/#ROOT#
+++ /dev/null
@@ -1,14 +0,0 @@
-chapter AFP
-
-session PAPP_Impossibility (AFP) = "HOL-Library" +
-  options [timeout = 900]
-  sessions
-    Randomised_Social_Choice
-  theories [document=false]
-    SAT_Replay
-  theories
-    PAPP_Impossibility
-  document_files
-    root.tex
-    root.bib
-
diff --git a/thys/PAPP_Impossibility/Anonymous_PAPP_Lowering.thy b/thys/PAPP_Impossibility/Anonymous_PAPP_Lowering.thy
--- a/thys/PAPP_Impossibility/Anonymous_PAPP_Lowering.thy
+++ b/thys/PAPP_Impossibility/Anonymous_PAPP_Lowering.thy
@@ -1,1374 +1,1309 @@
 (*
   File:     Anonymous_PAPP_Lowering.thy
   Author:   Manuel Eberl, University of Innsbruck 
 *)
 section \<open>Lowering P-APP Rules to Smaller Settings\<close>
 theory Anonymous_PAPP_Lowering
   imports Anonymous_PAPP
 begin
 
 text \<open>
   In this section, we prove a number of lemmas (corresponding to Lemma~1 in the paper) that allow
   us to take an anonymous P-APP rule with some additional properties (typically
   Cardinality-Strategyproofness and Weak Representation or Weak Proportional Representation) and 
   construct from it an anonymous P-APP rule for a different setting, i.e.\ different number of
   voters, parties, and/or result committee size.
 
   In the reverse direction, this also allows us to lift impossibility results from one setting 
   to another.
 \<close>
 
 subsection \<open>Preliminary Lemmas\<close>
 
 context card_stratproof_anon_papp
 begin
 
 text \<open>
   The following lemma is obtained by applying Strategyproofness repeatedly. It shows that
   if we have \<open>l\<close> voters with identical approval lists, then this entire group of voters has no
   incentive to submit wrong preferences. That is, the outcome they obtain by submitting their 
   genuine approval lists is weakly preferred by them over all outcomes obtained where these \<open>l\<close>
   voters submit any other preferences (and the remaining $n - l$ voters submit the same preferences
   as before).
 
   This is stronger than regular Strategyproofness, where we only demand that no voter has an
   incentive to submit wrong preferences \<^emph>\<open>unilaterally\<close> (and everyone else keeps the same
   preferences). Here we know that the entire group of \<open>l\<close> voters has no incentive to submit
   wrong preferences in coordination with one another.
 \<close>
 lemma proposition2:
   assumes "size B = l" "size A + l = n_voters"
   assumes "X \<noteq> {}" "X \<subseteq> parties" "{} \<notin># A+B" "\<forall>X'\<in>#A+B. X' \<subseteq> parties"
   shows   "r (replicate_mset l X + A) \<succeq>[Comm(X)] r (B + A)"
   using assms
 proof (induction l arbitrary: A B)
   case 0
   thus ?case
     by simp
 next
   case (Suc l A B)
   from Suc.prems have "set_mset B \<noteq> {}"
     by auto
   then obtain Y where Y: "Y \<in># B"
     by blast
   define B' where "B' = B - {#Y#}"
   define A' where "A' = A + {#Y#}"
   have [simp]: "size B' = l"
     using Suc.prems Y by (simp add: B'_def size_Diff_singleton)
   have [simp]: "size A' = n_voters - l"
     using Suc.prems Y by (simp add: A'_def)
 
   have "r (B' + A') \<preceq>[Comm(X)] r (replicate_mset l X + A')"
     by (rule Suc.IH) (use Suc.prems Y in \<open>auto simp: A'_def B'_def size_Diff_singleton\<close>)
   also have "B' + A' = B + A"
     using Y by (simp add: B'_def A'_def)
   also have "r (replicate_mset l X + A') \<preceq>[Comm(X)] r (replicate_mset (Suc l) X + A)"
   proof (rule not_manipulable'')
     show "replicate_mset (Suc l) X + A + {#Y#} = replicate_mset l X + A' + {#X#}"
       by (simp add: A'_def)
   next
     show "is_pref_profile (replicate_mset (Suc l) X + A)"
      using Suc.prems by unfold_locales (auto split: if_splits)
   next
     show "is_pref_profile (replicate_mset l X + A')"
       using Suc.prems Y by unfold_locales (auto split: if_splits simp: A'_def)
   qed
   finally show ?case .
 qed
 
 end
 
 
 context card_stratproof_weak_rep_anon_papp
 begin
 
 text \<open>
   In a setting with Weak Representation and Cardinality-Strategyproofness, Proposition 2 allows
   us to strengthen Weak Representation in the following way: Suppose we at least 
   $l \lfloor n/k\rfloor$ voters with the same approval list \<open>X\<close>, and \<open>X\<close> consists of at least \<open>l\<close>
   parties. Then at least \<open>l\<close> of the members of the result committee are in \<open>X\<close>.
 \<close>
 lemma proposition3:
   assumes "is_pref_profile A" "X \<subseteq> parties" "card X \<ge> l"
   assumes "committee_size > 0"
   assumes "count A X \<ge> l * \<lceil>n_voters / committee_size\<rceil>"
   shows   "size {# x\<in># r A. x \<in> X #} \<ge> l"
   using assms
 proof (induction l arbitrary: A X rule: less_induct)
   case (less l A X)
   interpret A: anon_papp_profile n_voters parties committee_size A
     by fact
   consider "l = 0" | "l = 1" | "l > 1"
     by force
   thus ?case
   proof cases
     assume "l = 0"
     thus ?thesis by simp
   next
     assume [simp]: "l = 1"
     define n where "n = count A X"
     with less.prems have "X \<noteq> {}"
       by auto
     then obtain x where x: "x \<in> X"
       by blast
     have "n \<le> size A"
       unfolding n_def by (rule count_le_size)
     hence "n \<le> n_voters"
       by (simp add: A.size_A)
 
     have "count A X > 0"
       by (rule Nat.gr0I) (use n_voters_pos less.prems in \<open>auto simp: field_simps\<close>)
     hence "X \<in># A"
       by force
     have [simp]: "replicate_mset n X \<subseteq># A"
       by (simp add: n_def flip: count_le_replicate_mset_subset_eq)
 
     define A'' where "A'' = A - replicate_mset n X"
     define A' where "A' = A'' + replicate_mset n {x}"
     interpret A': anon_papp_profile n_voters parties committee_size A'
       using A.A_nonempty A.A_subset A.size_A x \<open>X \<in># A\<close>
       by unfold_locales
          (fastforce simp: A'_def A''_def size_Diff_submset subset_mset.add_increasing2 
                     split: if_splits dest!: in_diffD)+
 
     have "x \<in># r A'"
     proof (rule weak_representation)
       show "is_pref_profile A'"
         by (fact A'.anon_papp_profile_axioms)
     next
       have "n_voters \<le> committee_size * n"
         using less.prems by (simp add: n_def ceiling_le_iff field_simps flip: of_nat_mult)
       also have "n \<le> count A' {x}"
         by (simp add: A'_def)
       finally show "n_voters \<le> committee_size * count A' {x}"
         by simp
     qed
     hence "1 \<le> count (r A') x"
       by simp
     also have "\<dots> = size {# y \<in># r A'. y = x #}"
       by simp
     also have "\<dots> \<le> size {# y \<in># r A'. y \<in> X #}"
       by (intro size_mset_mono multiset_filter_mono') (use x in auto)
 
     also have "r A' \<preceq>[Comm(X)] r A"
     proof -
       have "r (replicate_mset n {x} + A'') \<preceq>[Comm(X)] r (replicate_mset n X + A'')"
       proof (rule proposition2)
         show "{} \<notin># A'' + replicate_mset n {x}"
           using A'.A_nonempty by (auto simp: A'_def)
         show "\<forall>X'\<in>#A'' + replicate_mset n {x}. X' \<subseteq> parties"
           using A'.A_subset x by (auto simp: A'_def dest: in_diffD)
         show "size A'' + n = n_voters"
           using \<open>n \<le> n_voters\<close> by (auto simp: A''_def size_Diff_submset A.size_A)
       qed (use less.prems in auto)
       also have "replicate_mset n X + A'' = A"
         by (simp add: A''_def n_def flip: count_le_replicate_mset_subset_eq)
       finally show ?thesis
         by (simp add: A'_def add_ac)
     qed
     hence "size {# y \<in># r A'. y \<in> X #} \<le> size {# y \<in># r A. y \<in> X #}"
       by (simp add: committee_preference_def)
 
     finally show ?thesis
       by simp
 
   next
     assume l: "l > 1"
     
     define n where "n = count A X"
     have "n \<le> size A"
       unfolding n_def by (rule count_le_size)
     hence "n \<le> n_voters"
       by (simp add: A.size_A)
 
     define m where "m = nat (ceiling (n_voters / committee_size))"
     have "n_voters / committee_size \<le> m"
       unfolding m_def by linarith
     hence m: "n_voters \<le> committee_size * m"
       using \<open>committee_size > 0\<close> by (simp add: field_simps flip: of_nat_mult)
     have "real n_voters / real committee_size > 0"
       using n_voters_pos less.prems by auto
     hence m': "\<lceil>real n_voters / real committee_size\<rceil> = int m"
       by (simp add: m_def)
     have "1 * m \<le> l * m"
       using l by (intro mult_right_mono) auto
     also have "l * m \<le> n"
       using less.prems by (simp add: m' n_def flip: of_nat_mult)
     finally have "m \<le> n"
       by simp
 
     with less.prems l have "X \<noteq> {}"
       by auto
     then obtain x where x: "x \<in> X"
       by blast
     have "card (X - {x}) > 0"
       using less.prems x l by simp
     hence "X - {x} \<noteq> {}"
       by force
 
     have "count A X > 0"
       by (rule Nat.gr0I) (use n_voters_pos less.prems l in \<open>auto simp: field_simps mult_le_0_iff\<close>)
     hence "X \<in># A"
       by force
     have [simp]: "replicate_mset n X \<subseteq># A"
       by (simp add: n_def flip: count_le_replicate_mset_subset_eq)
 
     define A'' where "A'' = A - replicate_mset n X"
     define A' where "A' = A'' + replicate_mset m {x} + replicate_mset (n - m) (X - {x})"
     interpret A': anon_papp_profile n_voters parties committee_size A'
     proof
       show "Y \<subseteq> parties" if "Y \<in># A'" for Y
         using that A.A_subset x \<open>X \<in># A\<close>
         by (fastforce simp: A'_def A''_def dest!: in_diffD split: if_splits)
     next
       show "{} \<notin># A'"
         using A.A_nonempty x \<open>X \<in># A\<close> \<open>X - {x} \<noteq> {}\<close>
         by (auto simp: A'_def A''_def dest!: in_diffD split: if_splits)
     next
       show "size A' = n_voters"
         using \<open>m \<le> n\<close>
         by (auto simp: A'_def A''_def A.size_A subset_mset.add_increasing2 size_Diff_submset)
     qed
 
     have "x \<in># r A'"
     proof (rule weak_representation)
       show "is_pref_profile A'"
         by (fact A'.anon_papp_profile_axioms)
     next
       have "n_voters \<le> committee_size * m"
         by (fact m)
       also have "m \<le> count A' {x}"
         by (simp add: A'_def)
       finally show "n_voters \<le> committee_size * count A' {x}"
         by simp
     qed
     hence "1 \<le> count (r A') x"
       by simp
     also have "\<dots> = size {# y \<in># r A'. y = x #}"
       by simp
     finally have 1: "size {#y \<in># r A'. y = x#} \<ge> 1" .
 
     have 2: "size {# y \<in># r A'. y \<in> X - {x} #} \<ge> l - 1"
     proof (rule less.IH)
       have "int (l - 1) * \<lceil>real n_voters / real committee_size\<rceil> = int ((l - 1) * m)"
         by (auto simp add: m' not_less)
       also have "(l - 1) * m = l * m - m"
         by (simp add: algebra_simps)
       also have "l * m \<le> n"
         using less.prems by (simp add: m' n_def flip: of_nat_mult)
       hence "l * m - m \<le> n - m"
         by (meson diff_le_mono)
       also have "n - m \<le> count A' (X - {x})"
         by (simp add: A'_def A''_def)
       finally show "int (l - 1) * \<lceil>real n_voters / real committee_size\<rceil> \<le> int (count A' (X - {x}))"
         by simp
     qed (use l A'.anon_papp_profile_axioms x less.prems in \<open>auto\<close>)
 
     have "1 + (l - 1) \<le> size {#y \<in># r A'. y = x#} + size {#y \<in># r A'. y \<in> X - {x}#}"
       by (intro add_mono 1 2)
     also have "\<dots> = size ({#y \<in># r A'. y = x#} + {#y \<in># r A'. y \<in> X - {x}#})"
       by simp
     also have "{#y \<in># r A'. y = x#} + {#y \<in># r A'. y \<in> X - {x}#} =
                {#y \<in># r A'. y = x \<or> y \<in> X - {x}#}"
       by (rule filter_mset_disjunction [symmetric]) auto
     also have "(\<lambda>y. y = x \<or> y \<in> X - {x}) = (\<lambda>y. y \<in> X)"
       using x by auto
     also have "1 + (l - 1) = l"
       using l by simp
 
     also have "r A' \<preceq>[Comm(X)] r A"
     proof -
       have "r (replicate_mset m {x} + replicate_mset (n - m) (X - {x}) + A'') \<preceq>[Comm(X)] 
             r (replicate_mset n X + A'')"
       proof (rule proposition2)
         show " {} \<notin># A'' + (replicate_mset m {x} + replicate_mset (n - m) (X - {x}))"
           using A'.A_nonempty by (auto simp: A'_def)
         show "\<forall>X'\<in># A'' + (replicate_mset m {x} + replicate_mset (n - m) (X - {x})). X' \<subseteq> parties"
           using A'.A_subset x by (auto simp: A'_def dest: in_diffD)
         show "size A'' + n = n_voters"
           using \<open>n \<le> n_voters\<close> by (auto simp: A''_def size_Diff_submset A.size_A)
       qed (use less.prems l \<open>m \<le> n\<close> in auto)
       also have "replicate_mset n X + A'' = A"
         by (simp add: A''_def n_def flip: count_le_replicate_mset_subset_eq)
       finally show ?thesis
         by (simp add: A'_def add_ac)
     qed
     hence "size {# y \<in># r A'. y \<in> X #} \<le> size {# y \<in># r A. y \<in> X #}"
       by (simp add: committee_preference_def)
 
     finally show ?thesis
       by simp
   qed
 qed
 
 end
 
 
 subsection \<open>Dividing the number of voters\<close>
 
 text \<open>
   If we have a PAPP rule that satisfies weak representation and cardinality strategyproofness,
   for $ln$ voters, we can turn it into one for \<open>n\<close> voters.
   This is done by simply cloning each voter \<open>l\<close> times.
 
   Consequently, if we have an impossibility result for $n$ voters, it also holds for any
   integer multiple of \<open>n\<close>.
 \<close>
 locale divide_voters_card_stratproof_weak_rep_anon_papp =
   card_stratproof_weak_rep_anon_papp "l * n_voters" parties committee_size r
   for l n_voters parties committee_size r
 begin
 
 definition lift_profile :: "'a set multiset \<Rightarrow> 'a set multiset" where
   "lift_profile A = (\<Sum>X\<in>#A. replicate_mset l X)"
 
 sublocale lowered: anon_papp_election n_voters parties
   by standard (use n_voters_pos in auto)
 
 lemma l_pos: "l > 0"
   using n_voters_pos by auto
 
 lemma empty_in_lift_profile_iff [simp]: "{} \<in># lift_profile A \<longleftrightarrow> {} \<in># A"
   using l_pos by (auto simp: lift_profile_def)
 
 lemma set_mset_lift_profile [simp]: "set_mset (lift_profile A) = set_mset A"
   using l_pos by (auto simp: lift_profile_def)
 
 lemma size_lift_profile: "size (lift_profile A) = l * size A"
   by (simp add: size_mset_sum_mset lift_profile_def image_mset.compositionality o_def)
 
 lemma count_lift_profile [simp]: "count (lift_profile A) x = l * count A x"
   unfolding lift_profile_def by (induction A) auto
 
 lemma is_pref_profile_lift_profile [intro]:
   assumes "lowered.is_pref_profile A"
   shows   "is_pref_profile (lift_profile A)"
 proof -
   interpret anon_papp_profile n_voters parties committee_size A
     by fact
   show ?thesis
     using A_nonempty A_subset size_A
     by unfold_locales
        (auto simp: lift_profile_def size_mset_sum_mset image_mset.compositionality o_def)
 qed
 
 sublocale lowered: anon_papp n_voters parties committee_size "r \<circ> lift_profile"
 proof
   fix A assume "lowered.is_pref_profile A"
   hence "is_pref_profile (lift_profile A)"
     by blast
   hence "is_committee (r (lift_profile A))"
     using rule_wf by blast
   thus "lowered.is_committee ((r \<circ> lift_profile) A)"
     by simp
 qed
 
 sublocale lowered: weak_rep_anon_papp n_voters parties committee_size "r \<circ> lift_profile"
 proof
   fix A x
   assume A: "lowered.is_pref_profile A" and x: "n_voters \<le> committee_size * count A {x}"
   from A have A': "is_pref_profile (lift_profile A)"
     by blast
   from x have "l * n_voters \<le> l * (committee_size * count A {x})"
     by (rule mult_left_mono) auto
   also have "\<dots> = committee_size * count (lift_profile A) {x}"
     by simp
   finally have "x \<in># r (lift_profile A)"
     by (intro weak_representation A')
   thus "x \<in># (r \<circ> lift_profile) A"
     by simp
 qed
 
 sublocale lowered: card_stratproof_anon_papp n_voters parties committee_size "r \<circ> lift_profile"
 proof
   fix A X Y
   show "\<not>lowered.card_manipulable A X Y"
     unfolding lowered.card_manipulable_def
   proof (rule notI, elim conjE)
     assume A: "lowered.is_pref_profile A" and XY: "X \<in># A" "Y \<noteq> {}" "Y \<subseteq> parties"
     assume *: "(r \<circ> lift_profile) A \<prec>[lowered.committee_preference X] 
                (r \<circ> lift_profile) (A - {#X#} + {#Y#})"
     interpret anon_papp_profile n_voters parties committee_size A
       by fact
     have X: "X \<noteq> {}" "X \<subseteq> parties"
       using XY A_nonempty A_subset by auto
 
     define A' where "A' = A - {#X#}"
     have A': "A = A' + {#X#}"
       using XY by (simp add: A'_def)
 
     have "r (lift_profile A) \<prec>[committee_preference X]
           r (lift_profile (A - {#X#} + {#Y#}))"
       using * by simp
     also have "r (lift_profile (A - {#X#} + {#Y#})) \<preceq>[committee_preference X]
                r (lift_profile A - {#X#} + {#Y#})"
     proof -
       have "r (replicate_mset (l - 1) Y + (lift_profile A' + {#Y#})) \<preceq>[committee_preference X]
             r (replicate_mset (l - 1) X + (lift_profile A' + {#Y#}))"
       proof (rule proposition2)
         show "size (lift_profile A' + {#Y#}) + (l - 1) = l * n_voters"
           using XY l_pos n_voters_pos
           by (simp add: A'_def size_lift_profile size_Diff_singleton 
                         algebra_simps Suc_diff_le size_A)
       next
         show "{} \<notin># lift_profile A' + {#Y#} + replicate_mset (l - 1) Y"
           using XY A_nonempty by (auto simp: A'_def dest: in_diffD)
       next
         show "\<forall>X'\<in>#lift_profile A' + {#Y#} + replicate_mset (l - 1) Y. X' \<subseteq> parties"
           using XY A_subset by (auto simp: A'_def dest: in_diffD)
       qed (use X in auto)
       thus ?thesis
         by (simp add: A' replicate_mset_rec l_pos lift_profile_def)
     qed
     finally have "card_manipulable (lift_profile A) X Y"
       unfolding card_manipulable_def using XY A by auto
     with not_manipulable show False
       by blast
   qed
 qed
 
 sublocale lowered: card_stratproof_weak_rep_anon_papp n_voters parties committee_size "r \<circ> lift_profile"
   ..
 
 end
 
 
 locale divide_voters_card_stratproof_weak_prop_rep_anon_papp =
   card_stratproof_weak_prop_rep_anon_papp "l * n_voters" parties committee_size r
   for l n_voters parties committee_size r
 begin
 
 sublocale divide_voters_card_stratproof_weak_rep_anon_papp ..
 
 sublocale lowered: card_stratproof_weak_prop_rep_anon_papp
   n_voters parties committee_size "r \<circ> lift_profile"
 proof
   fix A x l'
   assume A: "lowered.is_pref_profile A" and x: "l' * n_voters \<le> committee_size * count A {x}"
   from A have A': "is_pref_profile (lift_profile A)"
     by blast
   from x have "l * (l' * n_voters) \<le> l * (committee_size * count A {x})"
     by (rule mult_left_mono) auto
   also have "\<dots> = committee_size * count (lift_profile A) {x}"
     by simp
   also have "l * (l' * n_voters) = l' * (l * n_voters)"
     by (simp add: algebra_simps)
   finally have "count (r (lift_profile A)) x \<ge> l'"
     by (intro weak_proportional_representation A')
   thus "count ((r \<circ> lift_profile) A) x \<ge> l'"
     by simp
 qed
 
 end
 
 
 
 subsection \<open>Decreasing the number of parties\<close>
 
 text \<open>
   If we have a PAPP rule that satisfies weak representation and cardinality strategyproofness,
   for $m$ parties, we can turn it into one for $m-1$ parties. This is done by simply
   duplicating one particular party (say \<open>x\<close>) in the preference profile, i.e.\ whenever
   \<open>x\<close> is part of an approval list, we add a clone of \<open>x\<close> (say \<open>y\<close>) as well. Should \<open>y\<close> then end up
   in the committee, we simply replace it with \<open>x\<close>.
 
   Consequently, if we have an impossibility result for $k$ parties, it also holds for
   $\geq m$ parties.
 \<close>
 locale remove_alt_card_stratproof_weak_rep_anon_papp =
   card_stratproof_weak_rep_anon_papp n_voters parties committee_size r
   for n_voters and parties :: "'a set" and committee_size r +
   fixes x y :: 'a
   assumes xy: "x \<in> parties" "y \<in> parties" "x \<noteq> y"
 begin
 
 definition lift_applist :: "'a set \<Rightarrow> 'a set" where
   "lift_applist X = (if x \<in> X then insert y X else X)"
 
 definition lift_profile :: "'a set multiset \<Rightarrow> 'a set multiset" where
   "lift_profile A = image_mset lift_applist A"
 
 definition lower_result where "lower_result C = image_mset (\<lambda>z. if z = y then x else z) C"
 
 definition lowered where "lowered = lower_result \<circ> r \<circ> lift_profile"
 
 
 lemma lift_profile_empty [simp]: "lift_profile {#} = {#}"
   by (simp add: lift_profile_def)
 
 lemma lift_profile_add_mset [simp]:
   "lift_profile (add_mset X A) = add_mset (lift_applist X) (lift_profile A)"
   by (simp add: lift_profile_def)
 
 lemma empty_in_lift_profile_iff [simp]: "{} \<in># lift_profile A \<longleftrightarrow> {} \<in># A"
   by (auto simp: lift_applist_def lift_profile_def)
 
 lemma size_lift_profile [simp]: "size (lift_profile A) = size A"
   by (simp add: lift_profile_def)
 
 lemma lift_applist_eq_self_iff [simp]: "lift_applist X = X \<longleftrightarrow> x \<notin> X \<or> y \<in> X"
   by (auto simp: lift_applist_def)
 
 lemma lift_applist_eq_self_iff' [simp]: "lift_applist (X - {y}) = X \<longleftrightarrow> (x \<in> X \<longleftrightarrow> y \<in> X)"
   by (cases "y \<in> X") (auto simp: lift_applist_def xy)
 
 lemma in_lift_applist_iff: "z \<in> lift_applist X \<longleftrightarrow> z \<in> X \<or> (z = y \<and> x \<in> X)"
   by (auto simp: lift_applist_def)
 
 lemma count_lift_profile:
   assumes "\<forall>Y\<in>#A. y \<notin> Y"
   shows   "count (lift_profile A) X = (if x \<in> X \<longleftrightarrow> y \<in> X then count A (X - {y}) else 0)"
   using assms xy by (induction A) (auto simp: lift_applist_def)
 
 lemma y_notin_lower_result [simp]: "y \<notin># lower_result C"
   using xy by (auto simp: lower_result_def)
 
 lemma lower_result_subset: "set_mset (lower_result C) \<subseteq> insert x (set_mset C - {y})"
   using xy by (auto simp: lower_result_def)
 
 lemma lower_result_subset': "set_mset C \<subseteq> parties \<Longrightarrow> set_mset (lower_result C) \<subseteq> parties"
   using xy by (auto simp: lower_result_def)
 
 lemma size_lower_result [simp]: "size (lower_result C) = size C"
   by (simp add: lower_result_def)
 
 lemma count_lower_result:
   "count (lower_result C) z =
      (if z = y then 0
       else if z = x then count C x + count C y
       else count C z)"
   using xy by (induction C) (auto simp: lower_result_def)
 
 lemma in_lower_result_iff:
   "z \<in># lower_result C \<longleftrightarrow> z \<noteq> y \<and> (z \<in># C \<or> (z = x \<and> y \<in># C))"
   unfolding lower_result_def using xy by (induction C) auto
 
 
 sublocale lowered: anon_papp_election n_voters "parties - {y}"
   by standard (use n_voters_pos xy in auto)
 
 lemma is_pref_profile_lift_profile [intro]:
   assumes "lowered.is_pref_profile A"
   shows   "is_pref_profile (lift_profile A)"
 proof -
   interpret anon_papp_profile n_voters "parties - {y}" committee_size A
     by fact
   show ?thesis
     using A_nonempty A_subset size_A
     by unfold_locales
        (auto simp: lift_profile_def lift_applist_def xy 
                    size_mset_sum_mset image_mset.compositionality o_def)
 qed
 
 sublocale lowered: anon_papp n_voters "parties - {y}" committee_size lowered
 proof
   fix A assume "lowered.is_pref_profile A"
   hence "is_pref_profile (lift_profile A)"
     by blast
   hence "is_committee (r (lift_profile A))"
     using rule_wf by blast
   thus "lowered.is_committee (lowered A)"
     unfolding lowered.is_committee_def is_committee_def lowered_def
     using lower_result_subset'[of "r (lift_profile A)"] by auto
 qed
 
 sublocale lowered: weak_rep_anon_papp n_voters "parties - {y}" committee_size lowered
 proof
   fix A z
   assume A: "lowered.is_pref_profile A" and z: "n_voters \<le> committee_size * count A {z}"
   interpret A: anon_papp_profile n_voters "parties - {y}" committee_size A
     by fact
   have "committee_size > 0"
     using z n_voters_pos by (intro Nat.gr0I) auto
 
   from A have A': "is_pref_profile (lift_profile A)"
     by blast
   have "count A {z} > 0"
     using z n_voters_pos by (intro Nat.gr0I) auto
   hence "{z} \<in># A"
     by simp
   hence z': "z \<in> parties - {y}"
     using A.A_subset z by auto
 
   define C where "C = r (lift_profile A)"
 
   show "z \<in># lowered A"
   proof (cases "z = x")
     case False
     have "n_voters \<le> committee_size * count A {z}"
       by fact
     also have "count A {z} \<le> count (lift_profile A) {z}"
       using A.A_subset z' False by (subst count_lift_profile) auto
     hence "committee_size * count A {z} \<le> committee_size * count (lift_profile A) {z}"
       by (intro mult_left_mono) auto
     finally have "z \<in># r (lift_profile A)"
       by (intro weak_representation A')
     thus "z \<in># lowered A"
       using False z' by (simp add: lowered_def in_lower_result_iff)
   next
     case [simp]: True
     have "1 \<le> size {#z \<in># C. z \<in> {x, y}#}"
       unfolding C_def
     proof (rule proposition3)
       have [simp]: "{x, y} - {y} = {x}"
         using xy by auto
       hence "n_voters \<le> committee_size * count (lift_profile A) {x, y}"
         using xy A.A_subset z by (subst count_lift_profile) auto
       thus "int 1 * \<lceil>real n_voters / real committee_size\<rceil> \<le> int (count (lift_profile A) {x, y})"
         using \<open>committee_size > 0\<close>
         by (auto simp: ceiling_le_iff field_simps simp flip: of_nat_mult)
     qed (use A' xy \<open>committee_size > 0\<close> in auto)
     also have "\<dots> = count C x + count C y"
       using xy by (induction C) auto
     also have "\<dots> = count (lowered A) x"
       using xy by (simp add: lowered_def count_lower_result C_def)
     finally show "z \<in># lowered A"
       by simp
   qed
 qed
 
 lemma filter_lower_result_eq:
   "y \<notin> X \<Longrightarrow> {#x \<in># lower_result C. x \<in> X#} = lower_result {#x \<in># C. x \<in> lift_applist X#}"
   by (induction C) (auto simp: lower_result_def lift_applist_def)
 
 sublocale lowered: card_stratproof_anon_papp n_voters "parties - {y}" committee_size lowered
 proof
   fix A X Y
   show "\<not>lowered.card_manipulable A X Y"
     unfolding lowered.card_manipulable_def
   proof (rule notI, elim conjE)
     assume A: "lowered.is_pref_profile A" and XY: "X \<in># A" "Y \<noteq> {}" "Y \<subseteq> parties - {y}"
     assume *: "lowered A \<prec>[lowered.committee_preference X] lowered (A - {#X#} + {#Y#})"
     interpret anon_papp_profile n_voters "parties - {y}" committee_size A
       by fact
     have X: "X \<noteq> {}" "X \<subseteq> parties - {y}"
       using XY A_nonempty A_subset by auto
     define A' where "A' = A - {#X#}"
     have A': "A = A' + {#X#}"
       using XY by (simp add: A'_def)
 
     from * have "size {#x \<in># lower_result (r (lift_profile A' + {#lift_applist X#})). x \<in> X#} <
                  size {#x \<in># lower_result (r (lift_profile A' + {#lift_applist Y#})). x \<in> X#}"
       by (simp add: lowered_def A' lowered.strong_committee_preference_iff)
     also have "{#x \<in># lower_result (r (lift_profile A' + {#lift_applist X#})). x \<in> X#} =
                lower_result {#x \<in># r (lift_profile A' + {#lift_applist X#}). x \<in> lift_applist X#}"
       using X by (subst filter_lower_result_eq) auto
     also have "{#x \<in># lower_result (r (lift_profile A' + {#lift_applist Y#})). x \<in> X#} =
                lower_result {#x \<in># r (lift_profile A' + {#lift_applist Y#}). x \<in> lift_applist X#}"
       using X by (subst filter_lower_result_eq) auto
     finally have "size {#x \<in># r (lift_profile A' + {#lift_applist X#}). x \<in> lift_applist X#} <
                   size {#x \<in># r (lift_profile A' + {#lift_applist Y#}). x \<in> lift_applist X#}"
       by simp
     hence "r (lift_profile A' + {#lift_applist X#}) \<prec>[committee_preference (lift_applist X)]
            r (lift_profile A' + {#lift_applist Y#})"
       by (simp add: strong_committee_preference_iff)
     moreover have "\<not>r (lift_profile A' + {#lift_applist X#}) \<prec>[committee_preference (lift_applist X)]
                     r (lift_profile A' + {#lift_applist Y#})"
     proof (rule not_manipulable' [where Y = "lift_applist Y"])
       have "is_pref_profile (lift_profile A)"
         using A by blast
       thus "is_pref_profile (lift_profile A' + {#lift_applist X#})"
         using A by (simp add: A')
     next
       have "is_pref_profile (lift_profile (A - {#X#} + {#Y#}))"
         using A  XY lowered.is_pref_profile_replace by blast
       thus "is_pref_profile (lift_profile A' + {#lift_applist Y#})"
         by (simp add: A')
     qed auto
     ultimately show False
       by contradiction
   qed
 qed
 
 sublocale lowered: card_stratproof_weak_rep_anon_papp n_voters "parties - {y}" committee_size lowered
   ..
 
 end
 
 
-(*
-locale remove_alt_card_stratproof_weak_prop_rep_anon_papp =
-  card_stratproof_weak_prop_rep_anon_papp n_voters parties committee_size r
-  for n_voters and parties :: "'a set" and committee_size r +
-  fixes x y :: 'a
-  assumes xy: "x \<in> parties" "y \<in> parties" "x \<noteq> y"
-begin
-
-sublocale remove_alt_card_stratproof_weak_rep_anon_papp
-  by standard (use xy in auto)
-
-sublocale lowered: weak_prop_rep_anon_papp n_voters "parties - {y}" committee_size lowered
-proof
-  fix A z l
-  assume A: "lowered.is_pref_profile A" and z: "l * n_voters \<le> committee_size * count A {z}"
-  interpret A: anon_papp_profile n_voters "parties - {y}" committee_size A
-    by fact
-
-  show "count (lowered A) z \<ge> l"
-  proof (cases "l = 0")
-    case True
-    thus ?thesis
-      by simp
-  next
-    case l: False
-
-    have "committee_size > 0"
-      using z n_voters_pos l by (intro Nat.gr0I) auto
-
-    from A have A': "is_pref_profile (lift_profile A)"
-      by blast
-    have "count A {z} > 0"
-      using z n_voters_pos l by (intro Nat.gr0I) auto
-    hence "{z} \<in># A"
-      by simp
-    hence z': "z \<in> parties - {y}"
-      using A.A_subset z by auto
-  
-    define C where "C = r (lift_profile A)"
-  
-    show ?thesis
-    proof (cases "z = x")
-      case False
-      have "l * n_voters \<le> committee_size * count A {z}"
-        by fact
-      also have "count A {z} \<le> count (lift_profile A) {z}"
-        using A.A_subset z' False by (subst count_lift_profile) auto
-      hence "committee_size * count A {z} \<le> committee_size * count (lift_profile A) {z}"
-        by (intro mult_left_mono) auto
-      finally have "count (r (lift_profile A)) z \<ge> l"
-        by (intro weak_proportional_representation A')
-      thus ?thesis
-        using False z' by (simp add: lowered_def count_lower_result)
-    next
-      case [simp]: True
-      show ?thesis
-        sorry
-    qed
-  qed
-qed
-
-end
-*)
-
-
 text \<open>
   The following lemma is now simply an iterated application of the above. This allows us to
   restrict a P-APP rule to any non-empty subset of parties.
 \<close>
 lemma card_stratproof_weak_rep_anon_papp_restrict_parties:
   assumes "card_stratproof_weak_rep_anon_papp n parties k r" "parties' \<subseteq> parties" "parties' \<noteq> {}"
   shows   "\<exists>r. card_stratproof_weak_rep_anon_papp n parties' k r"
 proof -
   have "finite parties"
   proof -
     interpret card_stratproof_weak_rep_anon_papp n parties k r
       by fact
     show ?thesis
       by (rule finite_parties)
   qed
   thus ?thesis
     using assms
   proof (induction parties arbitrary: r rule: finite_psubset_induct)
     case (psubset parties r)
     show ?thesis
     proof (cases "parties = parties'")
       case True
       thus ?thesis
         using psubset.prems by auto
     next
       case False
       obtain x where x: "x \<in> parties'"
         using psubset.prems by blast
       from False and psubset.prems have "parties - parties' \<noteq> {}"
         by auto
       then obtain y where y: "y \<in> parties - parties'"
         by blast
 
       interpret card_stratproof_weak_rep_anon_papp n parties k r
         by fact
       interpret remove_alt_card_stratproof_weak_rep_anon_papp n parties k r x y
         by standard (use x y psubset.prems in auto)
       show ?thesis
       proof (rule psubset.IH)
         show "parties - {y} \<subset> parties" and "parties' \<subseteq> parties - {y}" "parties' \<noteq> {}"
           using x y psubset.prems by auto
       next
         show "card_stratproof_weak_rep_anon_papp n (parties - {y}) k lowered"
           using lowered.card_stratproof_weak_rep_anon_papp_axioms .
       qed
     qed
   qed
 qed
 
 
 
 subsection \<open>Decreasing the committee size\<close>
 
 text \<open>
   If we have a PAPP rule that satisfies weak representation and cardinality strategyproofness,
   for $l(k+1)$ voters, $m+1$ parties, and a committee size of $k+1$, we can turn it into
   one for $lk$ voters, $m$ parties, and a committee size of $k$.
 
   This is done by again cloning a party \<open>x\<close> into a new party \<open>y\<close> and additionally
   adding \<open>l\<close> new voters whose preferences are \<open>{x, y}\<close>. We again replace any \<open>y\<close> occuring in the
   output committee with \<open>x\<close>. Weak representation then ensures that \<open>x\<close> occurs in the output
   at least once, and we then simply remove one \<open>x\<close> from the committee to obtain an output
   committee of size \<open>k - 1\<close>.
 
   Consequently, if we have an impossibility result for a committee size of $m$, we can
   extend it to a larger committee size, but at the cost of introducing a new party
   and new voters, and with a restriction on the number of voters.
 \<close>
 (* n / k = l *)
 locale decrease_committee_card_stratproof_weak_rep_anon_papp =
   card_stratproof_weak_rep_anon_papp "l * (k + 1)" "insert y parties" "k + 1" r
   for l k y and parties :: "'a set" and r +
   fixes x :: 'a
   assumes xy: "x \<in> parties" "y \<notin> parties"
   assumes k: "k > 0"
 begin
 
 definition lift_applist :: "'a set \<Rightarrow> 'a set" where
   "lift_applist X = (if x \<in> X then insert y X else X)"
 
 definition lift_profile :: "'a set multiset \<Rightarrow> 'a set multiset" where
   "lift_profile A = image_mset lift_applist A + replicate_mset l {x, y}"
 
 definition lower_result
   where "lower_result C = image_mset (\<lambda>z. if z = y then x else z) C - {#x#}"
 
 definition lowered where "lowered = lower_result \<circ> r \<circ> lift_profile"
 
 
 lemma l: "l > 0"
   using n_voters_pos by auto
 
 lemma x_neq_y [simp]: "x \<noteq> y" "y \<noteq> x"
   using xy by auto
 
 lemma lift_profile_empty [simp]: "lift_profile {#} = replicate_mset l {x, y}"
   by (simp add: lift_profile_def)
 
 lemma lift_profile_add_mset [simp]:
   "lift_profile (add_mset X A) = add_mset (lift_applist X) (lift_profile A)"
   by (simp add: lift_profile_def)
 
 lemma empty_in_lift_profile_iff [simp]: "{} \<in># lift_profile A \<longleftrightarrow> {} \<in># A"
   by (auto simp: lift_applist_def lift_profile_def)
 
 lemma size_lift_profile [simp]: "size (lift_profile A) = size A + l"
   by (simp add: lift_profile_def)
 
 lemma lift_applist_eq_self_iff [simp]: "lift_applist X = X \<longleftrightarrow> x \<notin> X \<or> y \<in> X"
   by (auto simp: lift_applist_def)
 
 lemma lift_applist_eq_self_iff' [simp]: "lift_applist (X - {y}) = X \<longleftrightarrow> (x \<in> X \<longleftrightarrow> y \<in> X)"
   by (cases "y \<in> X") (auto simp: lift_applist_def xy)
 
 lemma in_lift_applist_iff: "z \<in> lift_applist X \<longleftrightarrow> z \<in> X \<or> (z = y \<and> x \<in> X)"
   by (auto simp: lift_applist_def)
 
 lemma count_lift_profile:
   assumes "\<forall>Y\<in>#A. y \<notin> Y"
   shows   "count (lift_profile A) X =
              (if x \<in> X \<longleftrightarrow> y \<in> X then count A (X - {y}) else 0) +
              (if X = {x, y} then l else 0)"
   using assms xy by (induction A) (auto simp: lift_applist_def)
 
 
 
 lemma y_notin_lower_result [simp]: "y \<notin># lower_result C"
   using xy by (auto simp: lower_result_def dest: in_diffD)
 
 lemma lower_result_subset: "set_mset (lower_result C) \<subseteq> insert x (set_mset C - {y})"
   using xy by (auto simp: lower_result_def dest: in_diffD)
 
 lemma lower_result_subset': "set_mset C \<subseteq> insert y parties \<Longrightarrow> set_mset (lower_result C) \<subseteq> parties"
   by (rule order.trans[OF lower_result_subset]) (use xy in auto)
 
 lemma size_lower_result [simp]:
   assumes "x \<in># C \<or> y \<in># C"
   shows   "size (lower_result C) = size C - 1"
   using assms by (auto simp: lower_result_def size_Diff_singleton)
 
 lemma size_lower_result': "size (lower_result C) = size C - (if x \<in># C \<or> y \<in># C then 1 else 0)"
 proof -
   define f where "f = (\<lambda>C. image_mset (\<lambda>z. if z = y then x else z) C)"
   have "size (lower_result C) = size (f C - {#x#})"
     by (simp add: lower_result_def f_def)
   also have "\<dots> = size (f C) - (if x \<in># f C then 1 else 0)"
     by (simp add: diff_single_trivial size_Diff_singleton)
   finally show ?thesis
     by (auto simp: f_def)
 qed
 
 lemma count_lower_result:
   "count (lower_result C) z =
      (if z = y then 0
       else if z = x then count C x + count C y - 1
       else count C z)" (is "_ = ?rhs")
 proof -
   define f where "f = (\<lambda>C. image_mset (\<lambda>z. if z = y then x else z) C)"
   have "count (lower_result C) z = count (f C - {#x#}) z"
     by (simp add: lower_result_def f_def)
   also have "\<dots> = count (f C) z - (if z = x then 1 else 0)"
     by auto
   also have "count (f C) z = (if z = y then 0 else if z = x then count C x + count C y else count C z)"
     using xy by (induction C)  (auto simp: f_def)
   also have "\<dots> - (if z = x then 1 else 0) = ?rhs"
     by auto
   finally show ?thesis .
 qed
 
 lemma in_lower_resultD:
   "z \<in># lower_result C \<Longrightarrow> z = x \<or> z \<in># C"
   using xy by (auto simp: lower_result_def dest!: in_diffD)
 
 lemma in_lower_result_iff:
   "z \<in># lower_result C \<longleftrightarrow> z \<noteq> y \<and> (if z = x then count C x + count C y > 1 else z \<in># C)"
   (is "_ = ?rhs")
 proof -
   have "z \<in># lower_result C \<longleftrightarrow> count (lower_result C) z > 0"
     by auto
   also have "\<dots> \<longleftrightarrow> ?rhs"
     by (subst count_lower_result) auto
   finally show ?thesis .
 qed
 
 lemma filter_lower_result_eq:
   assumes "y \<notin> X"
   shows   "{#z \<in># lower_result C. z \<in> X#} = lower_result {#z \<in># C. z \<in> lift_applist X#}"
 proof -
   define f where "f = (\<lambda>C. {#if z = y then x else z. z \<in># C#})"
   have "lower_result {#z \<in># C. z \<in> lift_applist X#} = f {#z \<in># C. z \<in> lift_applist X#} - {#x#}"
     by (simp add: f_def lower_result_def)
   also have "f {#z \<in># C. z \<in> lift_applist X#} = {#z \<in># f C. z \<in> X#}"
     using assms by (induction C) (auto simp: f_def lift_applist_def)
   also have "\<dots> - {#x#} = {#z \<in># f C - {#x#}. z \<in> X#}"
     by (subst filter_diff_mset') auto
   also have "f C - {#x#} = lower_result C"
     by (simp add: f_def lower_result_def)
   finally show ?thesis ..
 qed
 
 
 sublocale lowered: anon_papp_election "l * k" parties k
   by standard (use n_voters_pos xy finite_parties k in auto)
 
 lemma is_pref_profile_lift_profile [intro]:
   assumes "lowered.is_pref_profile A"
   shows   "is_pref_profile (lift_profile A)"
 proof -
   interpret A: anon_papp_profile "l * k" parties k A
     by fact
   show ?thesis
     using A.A_nonempty A.A_subset A.size_A l
     by unfold_locales
        (auto simp: lift_profile_def lift_applist_def xy 
                    size_mset_sum_mset image_mset.compositionality o_def)
 qed
 
 lemma is_committee_lower_result:
   assumes "is_committee C" "x \<in># C \<or> y \<in># C"
   shows   "lowered.is_committee (lower_result C)"
   using assms unfolding is_committee_def lowered.is_committee_def
   using lower_result_subset'[of C] by auto
 
 lemma x_or_y_in_r_lift_profile:
   assumes "lowered.is_pref_profile A"
   shows   "x \<in># r (lift_profile A) \<or> y \<in># r (lift_profile A)"
 proof -
   interpret A: anon_papp_profile "l * k" parties k A
     by fact
   have "size {#z \<in># r (lift_profile A). z \<in> {x, y}#} \<ge> 1"
   proof (rule proposition3)
     have "real (l * (k + 1)) / real (k + 1) = real l"
       by (simp add: field_simps)
     also have "int 1 * \<lceil>\<dots>\<rceil> = int l"
       by simp
     also have "l \<le> count (lift_profile A) {x, y}"
       using xy A.A_subset by (subst count_lift_profile) auto
     finally show "int 1 * \<lceil>real (l * (k + 1)) / real (k + 1)\<rceil> \<le> int (count (lift_profile A) {x, y})"
       by simp
   next
     show "is_pref_profile (lift_profile A)"
       by (intro is_pref_profile_lift_profile) fact
   qed (use xy in auto)
   hence "{#z \<in># r (lift_profile A). z \<in> {x, y}#} \<noteq> {#}"
     by force
   thus ?thesis
     by auto
 qed
 
 sublocale lowered: anon_papp "l * k" parties k lowered
 proof
   fix A assume A: "lowered.is_pref_profile A"
   hence "is_pref_profile (lift_profile A)"
     by blast
   hence "is_committee (r (lift_profile A))"
     using rule_wf by blast
   thus "lowered.is_committee (lowered A)"
     unfolding lowered_def o_def using x_or_y_in_r_lift_profile[of A] A
     by (intro is_committee_lower_result) auto
 qed
 
 sublocale lowered: weak_rep_anon_papp "l * k" parties k lowered
 proof
   fix A z
   assume A: "lowered.is_pref_profile A" and z: "l * k \<le> k * count A {z}"
   interpret A: anon_papp_profile "l * k" "parties" k A
     by fact
 
   from A have A': "is_pref_profile (lift_profile A)"
     by blast
   have "count A {z} > 0"
     using z k n_voters_pos by (intro Nat.gr0I) auto
   hence "{z} \<in># A"
     by simp
   hence z': "z \<in> parties"
     using A.A_subset z by auto
   hence [simp]: "y \<noteq> z" "z \<noteq> y"
     using xy by auto
 
   define C where "C = r (lift_profile A)"
 
   show "z \<in># lowered A"
   proof (cases "z = x")
     case False
     have "l \<le> count A {z}"
       using z k by (simp add: algebra_simps)
     hence "l * (k + 1) \<le> (k + 1) * count A {z}"
       by (subst mult.commute, intro mult_right_mono) auto
     also have "count A {z} = count (lift_profile A) {z}"
       using False A.A_subset xy by (subst count_lift_profile) auto
     finally have "z \<in># r (lift_profile A)"
       by (intro weak_representation A')
     thus "z \<in># lowered A"
       using False by (auto simp: lowered_def in_lower_result_iff)
   next
     case [simp]: True
     from xy have [simp]: "{x, y} - {y} = {x}"
       by auto
 
     have "size {#z \<in># C. z \<in> {x, y}#} \<ge> 2"
       unfolding C_def
     proof (rule proposition3)
       have "real (l * (k + 1)) / real (k + 1) = l"
         unfolding of_nat_mult using k by (simp add: divide_simps)
       also have "int 2 * \<lceil>\<dots>\<rceil> = int (2 * l)"
         by simp
       also have "\<dots> \<le> count (lift_profile A) {x, y}"
         using z k xy A.A_subset by (subst count_lift_profile) auto
       finally show "int 2 * \<lceil>real (l * (k + 1)) / real (k + 1)\<rceil> \<le> \<dots>" .
     qed (use A' xy in auto)
     also have "size {#z \<in># C. z \<in> {x, y}#} = count C x + count C y"
       by (induction C) auto
     finally have "x \<in># lower_result C"
       by (subst in_lower_result_iff) auto
     thus "z \<in># lowered A"
       by (simp add: lowered_def C_def)
   qed
 qed
 
 sublocale lowered: card_stratproof_anon_papp "l * k" parties k lowered
 proof
   fix A X Y
   show "\<not>lowered.card_manipulable A X Y"
     unfolding lowered.card_manipulable_def
   proof (rule notI, elim conjE)
     assume A: "lowered.is_pref_profile A" and XY: "X \<in># A" "Y \<noteq> {}" "Y \<subseteq> parties"
     assume *: "lowered A \<prec>[lowered.committee_preference X] lowered (A - {#X#} + {#Y#})"
     interpret anon_papp_profile "l * k" "parties" k A
       by fact
     have X: "X \<noteq> {}" "X \<subseteq> parties"
       using XY A_nonempty A_subset by auto
     define A' where "A' = A - {#X#}"
     have A': "A = A' + {#X#}"
       using XY by (simp add: A'_def)
     from xy X XY have [simp]: "y \<notin> X" "y \<notin> Y"
       by auto
 
     define Al1 where "Al1 = lift_profile A"
     define Al2 where "Al2 = lift_profile (A' + {#Y#})"
     have A'_plus_Y: "lowered.is_pref_profile (A' + {#Y#})"
       unfolding A'_def using A XY lowered.is_pref_profile_replace by blast
     have Al1: "is_pref_profile Al1"
       unfolding Al1_def using A by blast
     have Al2: "is_pref_profile Al2"
       unfolding Al2_def unfolding A'_def using A XY lowered.is_pref_profile_replace by blast
 
     have size_aux: "size (lower_result {#x \<in># r (lift_profile A). x \<in> lift_applist X#}) =
                     size {#x \<in># r (lift_profile A). x \<in> lift_applist X#} - (if x \<in> X then 1 else 0)"
       if A: "lowered.is_pref_profile A" for A
       using x_or_y_in_r_lift_profile[OF A] 
       by (subst size_lower_result') (auto simp: lift_applist_def)
 
     from * have "size {#x \<in># lower_result (r Al1). x \<in> X#} <
                  size {#x \<in># lower_result (r Al2). x \<in> X#}"
       by (simp add: Al1_def Al2_def lowered_def A' lowered.strong_committee_preference_iff)
     also have "{#x \<in># lower_result (r Al1). x \<in> X#} = lower_result {#x \<in># r Al1. x \<in> lift_applist X#}"
       using X xy by (subst filter_lower_result_eq) auto
     also have "{#x \<in># lower_result (r Al2). x \<in> X#} = lower_result {#x \<in># r Al2. x \<in> lift_applist X#}"
       using X xy by (subst filter_lower_result_eq) auto
     also have "size (lower_result {#x \<in># r Al1. x \<in> lift_applist X#}) =
                size {#x \<in># r Al1. x \<in> lift_applist X#} - (if x \<in> X then 1 else 0)"
       unfolding Al1_def by (rule size_aux) fact
     also have "size (lower_result {#x \<in># r Al2. x \<in> lift_applist X#}) =
                size {#x \<in># r Al2. x \<in> lift_applist X#} - (if x \<in> X then 1 else 0)"
       unfolding Al2_def by (rule size_aux) fact
     finally have "size {#x \<in># r Al1. x \<in> lift_applist X#} < size {#x \<in># r Al2. x \<in> lift_applist X#}"
       by auto
     hence "r Al1 \<prec>[committee_preference (lift_applist X)] r Al2"
       by (simp add: strong_committee_preference_iff)
 
     moreover have "\<not>r Al1 \<prec>[committee_preference (lift_applist X)] r Al2"
       by (rule not_manipulable' [where Y = "lift_applist Y"])
          (use Al1 Al2 in \<open>auto simp: Al1_def Al2_def A'\<close>)
 
     ultimately show False
       by contradiction
   qed
 qed
 
 sublocale lowered: card_stratproof_weak_rep_anon_papp "l * k" parties k lowered
   ..
 
 end
 
 
 text \<open>
   For Weak \<^emph>\<open>Proportional\<close> Representation, the lowering argument to decrease the committee size
   is somewhat easier since it does not involve adding a new party; instead, we simply
   add \<open>l\<close> new voters whose preferences are \<open>{x}\<close>.
 \<close>
 locale decrease_committee_card_stratproof_weak_prop_rep_anon_papp =
   card_stratproof_weak_prop_rep_anon_papp "l * (k + 1)" parties "k + 1" r
   for l k and parties :: "'a set" and r +
   fixes x :: 'a
   assumes x: "x \<in> parties"
   assumes k: "k > 0"
 begin
 
 definition lift_profile :: "'a set multiset \<Rightarrow> 'a set multiset" where
   "lift_profile A = A + replicate_mset l {x}"
 
 definition lower_result
   where "lower_result C = C - {#x#}"
 
 definition lowered where "lowered = lower_result \<circ> r \<circ> lift_profile"
 
 
 lemma l: "l > 0"
   using n_voters_pos by auto
 
 lemma lift_profile_empty [simp]: "lift_profile {#} = replicate_mset l {x}"
   by (simp add: lift_profile_def)
 
 lemma lift_profile_add_mset [simp]:
   "lift_profile (add_mset X A) = add_mset X (lift_profile A)"
   by (simp add: lift_profile_def)
 
 lemma empty_in_lift_profile_iff [simp]: "{} \<in># lift_profile A \<longleftrightarrow> {} \<in># A"
   by (auto simp: lift_profile_def)
 
 lemma size_lift_profile [simp]: "size (lift_profile A) = size A + l"
   by (simp add: lift_profile_def)
 
 lemma count_lift_profile:
   "count (lift_profile A) X = count A X + (if X = {x} then l else 0)"
   by (auto simp: lift_profile_def)
 
 
 lemma size_lower_result [simp]:
   assumes "x \<in># C"
   shows   "size (lower_result C) = size C - 1"
   using assms by (auto simp: lower_result_def size_Diff_singleton)
 
 lemma size_lower_result': "size (lower_result C) = size C - (if x \<in># C then 1 else 0)"
   by (induction C) (auto simp: lower_result_def size_Diff_singleton)
 
 lemma count_lower_result:
   "count (lower_result C) z = count C z - (if z = x then 1 else 0)"
   by (auto simp: lower_result_def)
 
 lemma in_lower_resultD:
   "z \<in># lower_result C \<Longrightarrow> z \<in># C"
   by (auto simp: lower_result_def dest!: in_diffD)
 
 lemma in_lower_result_iff:
   "z \<in># lower_result C \<longleftrightarrow> (if z = x then count C x > 1 else z \<in># C)"
   (is "_ = ?rhs")
 proof -
   have "z \<in># lower_result C \<longleftrightarrow> count (lower_result C) z > 0"
     by auto
   also have "\<dots> \<longleftrightarrow> ?rhs"
     by (subst count_lower_result) auto
   finally show ?thesis .
 qed
 
 
 sublocale lowered: anon_papp_election "l * k" parties k
   by standard (use n_voters_pos finite_parties k in auto)
 
 lemma is_pref_profile_lift_profile [intro]:
   assumes "lowered.is_pref_profile A"
   shows   "is_pref_profile (lift_profile A)"
 proof -
   interpret A: anon_papp_profile "l * k" parties k A
     by fact
   show ?thesis
     using A.A_nonempty A.A_subset A.size_A l
     by unfold_locales
        (auto simp: lift_profile_def x size_mset_sum_mset image_mset.compositionality o_def)
 qed
 
 lemma is_committee_lower_result:
   assumes "is_committee C" "x \<in># C"
   shows   "lowered.is_committee (lower_result C)"
   using assms unfolding is_committee_def lowered.is_committee_def
   by (auto simp: lower_result_def size_Diff_singleton dest: in_diffD)
 
 lemma x_in_r_lift_profile:
   assumes "lowered.is_pref_profile A"
   shows   "x \<in># r (lift_profile A)"
 proof (rule weak_representation)
   show "is_pref_profile (lift_profile A)"
     using assms by blast
 next
   have "(k + 1) * l \<le> (k + 1) * count (lift_profile A) {x}"
     by (intro mult_left_mono) (auto simp: count_lift_profile)
   thus "l * (k + 1) \<le> (k + 1) * count (lift_profile A) {x}"
     by (simp add: algebra_simps)
 qed
 
 sublocale lowered: anon_papp "l * k" parties k lowered
 proof
   fix A assume A: "lowered.is_pref_profile A"
   hence "is_pref_profile (lift_profile A)"
     by blast
   hence "is_committee (r (lift_profile A))"
     using rule_wf by blast
   thus "lowered.is_committee (lowered A)"
     unfolding lowered_def o_def using x_in_r_lift_profile[of A] A
     by (intro is_committee_lower_result) auto
 qed
 
 sublocale lowered: weak_prop_rep_anon_papp "l * k" parties k lowered
 proof
   fix A z l'
   assume A: "lowered.is_pref_profile A" and z: "l' * (l * k) \<le> k * count A {z}"
   interpret A: anon_papp_profile "l * k" "parties" k A
     by fact
 
   show "count (lowered A) z \<ge> l'"
   proof (cases "l' > 0")
     case False
     thus ?thesis by auto
   next
     case l: True
 
     from A have A': "is_pref_profile (lift_profile A)"
       by blast
     have "count A {z} > 0"
       using z k n_voters_pos l by (intro Nat.gr0I) auto
     hence "{z} \<in># A"
       by simp
     hence z': "z \<in> parties"
       using A.A_subset z by auto
   
     define C where "C = r (lift_profile A)"
   
     show "count (lowered A) z \<ge> l'"
     proof (cases "z = x")
       case False
       have "l' * l \<le> count A {z}"
         using z k by (simp add: algebra_simps)
       hence "l' * l * (k + 1) \<le> (k + 1) * count A {z}"
         by (subst mult.commute, intro mult_right_mono) auto
       also have "count A {z} = count (lift_profile A) {z}"
         using False A.A_subset by (subst count_lift_profile) auto
       finally have "count (r (lift_profile A)) z \<ge> l'"
         by (intro weak_proportional_representation A') (auto simp: algebra_simps)
       thus "l' \<le> count (lowered A) z"
         using False by (simp add: lowered_def lower_result_def)
     next
       case [simp]: True
       have "l' * l \<le> count A {x}"
         using z k by (simp add: algebra_simps)
       hence "l' * l * (k + 1) \<le> (k + 1) * count A {x}"
         by (subst mult.commute, intro mult_right_mono) auto
       also have "\<dots> + (k + 1) * l = (k + 1) * count (lift_profile A) {x}"
         by (simp add: count_lift_profile algebra_simps)
       finally have "(l' + 1) * (l * (k + 1)) \<le> (k + 1) * count (lift_profile A) {x}"
         by (simp add: algebra_simps)
       hence "count (r (lift_profile A)) x \<ge> l' + 1"
         by (intro weak_proportional_representation A')
       thus "l' \<le> count (lowered A) z"
         by (simp add: lowered_def lower_result_def)
     qed
   qed
 qed
 
 sublocale lowered: card_stratproof_anon_papp "l * k" parties k lowered
 proof
   fix A X Y
   show "\<not>lowered.card_manipulable A X Y"
     unfolding lowered.card_manipulable_def
   proof (rule notI, elim conjE)
     assume A: "lowered.is_pref_profile A" and XY: "X \<in># A" "Y \<noteq> {}" "Y \<subseteq> parties"
     assume *: "lowered A \<prec>[lowered.committee_preference X] lowered (A - {#X#} + {#Y#})"
     interpret anon_papp_profile "l * k" "parties" k A
       by fact
     have X: "X \<noteq> {}" "X \<subseteq> parties"
       using XY A_nonempty A_subset by auto
     define A' where "A' = A - {#X#}"
     have A': "A = A' + {#X#}"
       using XY by (simp add: A'_def)
 
     define Al1 where "Al1 = lift_profile A"
     define Al2 where "Al2 = lift_profile (A' + {#Y#})"
     have A'_plus_Y: "lowered.is_pref_profile (A' + {#Y#})"
       unfolding A'_def using A XY lowered.is_pref_profile_replace by blast
     have Al1: "is_pref_profile Al1"
       unfolding Al1_def using A by blast
     have Al2: "is_pref_profile Al2"
       unfolding Al2_def unfolding A'_def using A XY lowered.is_pref_profile_replace by blast
 
     have size_aux: "size (lower_result {#x \<in># r (lift_profile A). x \<in> X#}) =
                     size {#x \<in># r (lift_profile A). x \<in> X#} - (if x \<in> X then 1 else 0)"
       if A: "lowered.is_pref_profile A" for A
       using x_in_r_lift_profile[OF A]  by (subst size_lower_result') auto
 
     from * have "size {#x \<in># lower_result (r Al1). x \<in> X#} <
                  size {#x \<in># lower_result (r Al2). x \<in> X#}"
       by (simp add: Al1_def Al2_def lowered_def A' lowered.strong_committee_preference_iff)
     also have "{#x \<in># lower_result (r Al1). x \<in> X#} = lower_result {#x \<in># r Al1. x \<in> X#}"
       using X x unfolding lower_result_def by (subst filter_diff_mset') auto
     also have "{#x \<in># lower_result (r Al2). x \<in> X#} = lower_result {#x \<in># r Al2. x \<in> X#}"
       using X x unfolding lower_result_def by (subst filter_diff_mset') auto
     also have "size (lower_result {#x \<in># r Al1. x \<in> X#}) =
                size {#x \<in># r Al1. x \<in> X#} - (if x \<in> X then 1 else 0)"
       unfolding Al1_def by (rule size_aux) fact
     also have "size (lower_result {#x \<in># r Al2. x \<in> X#}) =
                size {#x \<in># r Al2. x \<in> X#} - (if x \<in> X then 1 else 0)"
       unfolding Al2_def by (rule size_aux) fact
     finally have "size {#x \<in># r Al1. x \<in> X#} < size {#x \<in># r Al2. x \<in> X#}"
       by auto
     hence "r Al1 \<prec>[committee_preference X] r Al2"
       by (simp add: strong_committee_preference_iff)
 
     moreover have "\<not>r Al1 \<prec>[committee_preference X] r Al2"
       by (rule not_manipulable' [where Y = "Y"])
          (use Al1 Al2 in \<open>auto simp: Al1_def Al2_def A'\<close>)
 
     ultimately show False
       by contradiction
   qed
 qed
 
 sublocale lowered: card_stratproof_weak_prop_rep_anon_papp "l * k" parties k lowered
   ..
 
 end
 
 end
diff --git a/thys/PAPP_Impossibility/ROOT b/thys/PAPP_Impossibility/ROOT
--- a/thys/PAPP_Impossibility/ROOT
+++ b/thys/PAPP_Impossibility/ROOT
@@ -1,15 +1,14 @@
 chapter AFP
 
-session PAPP_Impossibility (AFP) = "HOL" +
+session PAPP_Impossibility (AFP) = "HOL-Library" +
   options [timeout = 900]
   sessions
-    "HOL-Library"
     Randomised_Social_Choice
   theories [document=false]
     SAT_Replay
   theories
     PAPP_Impossibility
   document_files
     root.tex
     root.bib
 
diff --git a/web/index.xml b/web/index.xml
--- a/web/index.xml
+++ b/web/index.xml
@@ -1,13112 +1,13112 @@
 <?xml version="1.0" encoding="utf-8" standalone="yes"?>
 <rss version="2.0" xmlns:atom="http://www.w3.org/2005/Atom">
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     <title>Archive of Formal Proofs</title>
     <link>/</link>
     <description>Recent content on Archive of Formal Proofs</description>
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       <title>Combinatorial Enumeration Algorithms</title>
       <link>/entries/Combinatorial_Enumeration_Algorithms.html</link>
       <pubDate>Fri, 11 Nov 2022 00:00:00 +0000</pubDate>
       
       <guid>/entries/Combinatorial_Enumeration_Algorithms.html</guid>
       <description></description>
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       <title>The Balog–Szemerédi–Gowers Theorem</title>
       <link>/entries/Balog_Szemeredi_Gowers.html</link>
       <pubDate>Fri, 11 Nov 2022 00:00:00 +0000</pubDate>
       
       <guid>/entries/Balog_Szemeredi_Gowers.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>The Incompatibility of Strategy-Proofness and Representation in Party-Approval Multi-Winner Elections</title>
       <link>/entries/PAPP_Impossibility.html</link>
       <pubDate>Thu, 10 Nov 2022 00:00:00 +0000</pubDate>
       
       <guid>/entries/PAPP_Impossibility.html</guid>
       <description></description>
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     <item>
       <title>Verification of Query Optimization Algorithms</title>
       <link>/entries/Query_Optimization.html</link>
       <pubDate>Tue, 04 Oct 2022 00:00:00 +0000</pubDate>
       
       <guid>/entries/Query_Optimization.html</guid>
       <description></description>
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     <item>
       <title>Maximum Segment Sum</title>
       <link>/entries/Maximum_Segment_Sum.html</link>
       <pubDate>Thu, 29 Sep 2022 00:00:00 +0000</pubDate>
       
       <guid>/entries/Maximum_Segment_Sum.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Undirected Graph Theory</title>
       <link>/entries/Undirected_Graph_Theory.html</link>
       <pubDate>Thu, 29 Sep 2022 00:00:00 +0000</pubDate>
       
       <guid>/entries/Undirected_Graph_Theory.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Making Arbitrary Relational Calculus Queries Safe-Range</title>
       <link>/entries/Safe_Range_RC.html</link>
       <pubDate>Wed, 28 Sep 2022 00:00:00 +0000</pubDate>
       
       <guid>/entries/Safe_Range_RC.html</guid>
       <description></description>
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     <item>
       <title>Stalnaker&#39;s Epistemic Logic</title>
       <link>/entries/Stalnaker_Logic.html</link>
       <pubDate>Fri, 23 Sep 2022 00:00:00 +0000</pubDate>
       
       <guid>/entries/Stalnaker_Logic.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>p-adic Fields and p-adic Semialgebraic Sets</title>
       <link>/entries/Padic_Field.html</link>
       <pubDate>Thu, 22 Sep 2022 00:00:00 +0000</pubDate>
       
       <guid>/entries/Padic_Field.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Risk-Free Lending</title>
       <link>/entries/Risk_Free_Lending.html</link>
       <pubDate>Sun, 18 Sep 2022 00:00:00 +0000</pubDate>
       
       <guid>/entries/Risk_Free_Lending.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Soundness and Completeness of Implicational Logic</title>
       <link>/entries/Implicational_Logic.html</link>
       <pubDate>Tue, 13 Sep 2022 00:00:00 +0000</pubDate>
       
       <guid>/entries/Implicational_Logic.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>CRYSTALS-Kyber</title>
       <link>/entries/CRYSTALS-Kyber.html</link>
       <pubDate>Thu, 08 Sep 2022 00:00:00 +0000</pubDate>
       
       <guid>/entries/CRYSTALS-Kyber.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Unbounded Separation Logic</title>
       <link>/entries/Separation_Logic_Unbounded.html</link>
       <pubDate>Mon, 05 Sep 2022 00:00:00 +0000</pubDate>
       
       <guid>/entries/Separation_Logic_Unbounded.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Khovanskii&amp;#x27;s Theorem</title>
       <link>/entries/Khovanskii_Theorem.html</link>
       <pubDate>Fri, 02 Sep 2022 00:00:00 +0000</pubDate>
       
       <guid>/entries/Khovanskii_Theorem.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>The Hales–Jewett Theorem</title>
       <link>/entries/Hales_Jewett.html</link>
       <pubDate>Fri, 02 Sep 2022 00:00:00 +0000</pubDate>
       
       <guid>/entries/Hales_Jewett.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Number Theoretic Transform</title>
       <link>/entries/Number_Theoretic_Transform.html</link>
       <pubDate>Thu, 18 Aug 2022 00:00:00 +0000</pubDate>
       
       <guid>/entries/Number_Theoretic_Transform.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Correctness of a Set-based Algorithm for Computing Strongly Connected Components of a Graph</title>
       <link>/entries/SCC_Bloemen_Sequential.html</link>
       <pubDate>Wed, 17 Aug 2022 00:00:00 +0000</pubDate>
       
       <guid>/entries/SCC_Bloemen_Sequential.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>From THE BOOK: Two Squares via Involutions</title>
       <link>/entries/Involutions2Squares.html</link>
       <pubDate>Mon, 15 Aug 2022 00:00:00 +0000</pubDate>
       
       <guid>/entries/Involutions2Squares.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Verified Complete Test Strategies for Finite State Machines</title>
       <link>/entries/FSM_Tests.html</link>
       <pubDate>Tue, 09 Aug 2022 00:00:00 +0000</pubDate>
       
       <guid>/entries/FSM_Tests.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Nano JSON: Working with JSON formatted data in Isabelle/HOL and Isabelle/ML</title>
       <link>/entries/Nano_JSON.html</link>
       <pubDate>Fri, 29 Jul 2022 00:00:00 +0000</pubDate>
       
       <guid>/entries/Nano_JSON.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Isabelle/Solidity: A deep Embedding of Solidity in Isabelle/HOL</title>
       <link>/entries/Solidity.html</link>
       <pubDate>Mon, 18 Jul 2022 00:00:00 +0000</pubDate>
       
       <guid>/entries/Solidity.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Simultaneous diagonalization of pairwise commuting Hermitian matrices</title>
       <link>/entries/Commuting_Hermitian.html</link>
       <pubDate>Mon, 18 Jul 2022 00:00:00 +0000</pubDate>
       
       <guid>/entries/Commuting_Hermitian.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Pólya’s Proof of the Weighted Arithmetic–Geometric Mean Inequality</title>
       <link>/entries/Weighted_Arithmetic_Geometric_Mean.html</link>
       <pubDate>Mon, 11 Jul 2022 00:00:00 +0000</pubDate>
       
       <guid>/entries/Weighted_Arithmetic_Geometric_Mean.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>A Reuse-Based Multi-Stage Compiler Verification for Language IMP</title>
       <link>/entries/IMP_Compiler_Reuse.html</link>
       <pubDate>Sun, 10 Jul 2022 00:00:00 +0000</pubDate>
       
       <guid>/entries/IMP_Compiler_Reuse.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Real-Time Double-Ended Queue</title>
       <link>/entries/Real_Time_Deque.html</link>
       <pubDate>Thu, 23 Jun 2022 00:00:00 +0000</pubDate>
       
       <guid>/entries/Real_Time_Deque.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Boolos&#39;s Curious Inference in Isabelle/HOL</title>
       <link>/entries/Boolos_Curious_Inference.html</link>
       <pubDate>Mon, 20 Jun 2022 00:00:00 +0000</pubDate>
       
       <guid>/entries/Boolos_Curious_Inference.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Finite Fields</title>
       <link>/entries/Finite_Fields.html</link>
       <pubDate>Wed, 08 Jun 2022 00:00:00 +0000</pubDate>
       
       <guid>/entries/Finite_Fields.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>IsaNet: Formalization of a Verification Framework for Secure Data Plane Protocols</title>
       <link>/entries/IsaNet.html</link>
       <pubDate>Wed, 08 Jun 2022 00:00:00 +0000</pubDate>
       
       <guid>/entries/IsaNet.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Diophantine Equations and the DPRM Theorem</title>
       <link>/entries/DPRM_Theorem.html</link>
       <pubDate>Mon, 06 Jun 2022 00:00:00 +0000</pubDate>
       
       <guid>/entries/DPRM_Theorem.html</guid>
       <description></description>
     </item>
     
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       <title>Reducing Rewrite Properties to Properties on Ground Terms</title>
       <link>/entries/Rewrite_Properties_Reduction.html</link>
       <pubDate>Thu, 02 Jun 2022 00:00:00 +0000</pubDate>
       
       <guid>/entries/Rewrite_Properties_Reduction.html</guid>
       <description></description>
     </item>
     
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       <title>A Restricted Definition of the Magic Wand to Soundly Combine Fractions of a Wand</title>
       <link>/entries/Combinable_Wands.html</link>
       <pubDate>Mon, 30 May 2022 00:00:00 +0000</pubDate>
       
       <guid>/entries/Combinable_Wands.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>The Plünnecke-Ruzsa Inequality</title>
       <link>/entries/Pluennecke_Ruzsa_Inequality.html</link>
       <pubDate>Thu, 26 May 2022 00:00:00 +0000</pubDate>
       
       <guid>/entries/Pluennecke_Ruzsa_Inequality.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Formalization of a Framework for the Sound Automation of Magic Wands</title>
       <link>/entries/Package_logic.html</link>
       <pubDate>Wed, 18 May 2022 00:00:00 +0000</pubDate>
       
       <guid>/entries/Package_logic.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Clique is not solvable by monotone circuits of polynomial size</title>
       <link>/entries/Clique_and_Monotone_Circuits.html</link>
       <pubDate>Sun, 08 May 2022 00:00:00 +0000</pubDate>
       
       <guid>/entries/Clique_and_Monotone_Circuits.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Fisher&#39;s Inequality: Linear Algebraic Proof Techniques for Combinatorics</title>
       <link>/entries/Fishers_Inequality.html</link>
       <pubDate>Thu, 21 Apr 2022 00:00:00 +0000</pubDate>
       
       <guid>/entries/Fishers_Inequality.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Digit Expansions</title>
       <link>/entries/Digit_Expansions.html</link>
       <pubDate>Wed, 20 Apr 2022 00:00:00 +0000</pubDate>
       
       <guid>/entries/Digit_Expansions.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>The Generalized Multiset Ordering is NP-Complete</title>
       <link>/entries/Multiset_Ordering_NPC.html</link>
       <pubDate>Wed, 20 Apr 2022 00:00:00 +0000</pubDate>
       
       <guid>/entries/Multiset_Ordering_NPC.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>The Sophomore&#39;s Dream</title>
       <link>/entries/Sophomores_Dream.html</link>
       <pubDate>Sun, 10 Apr 2022 00:00:00 +0000</pubDate>
       
       <guid>/entries/Sophomores_Dream.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>A Combinator Library for Prefix-Free Codes</title>
       <link>/entries/Prefix_Free_Code_Combinators.html</link>
       <pubDate>Fri, 08 Apr 2022 00:00:00 +0000</pubDate>
       
       <guid>/entries/Prefix_Free_Code_Combinators.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Formalization of Randomized Approximation Algorithms for Frequency Moments</title>
       <link>/entries/Frequency_Moments.html</link>
       <pubDate>Fri, 08 Apr 2022 00:00:00 +0000</pubDate>
       
       <guid>/entries/Frequency_Moments.html</guid>
       <description></description>
     </item>
     
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       <title>Constructing the Reals as Dedekind Cuts of Rationals</title>
       <link>/entries/Dedekind_Real.html</link>
       <pubDate>Thu, 24 Mar 2022 00:00:00 +0000</pubDate>
       
       <guid>/entries/Dedekind_Real.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Ackermann&#39;s Function Is Not Primitive Recursive</title>
       <link>/entries/Ackermanns_not_PR.html</link>
       <pubDate>Wed, 23 Mar 2022 00:00:00 +0000</pubDate>
       
       <guid>/entries/Ackermanns_not_PR.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>A Naive Prover for First-Order Logic</title>
       <link>/entries/FOL_Seq_Calc3.html</link>
       <pubDate>Tue, 22 Mar 2022 00:00:00 +0000</pubDate>
       
       <guid>/entries/FOL_Seq_Calc3.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>A Proof from THE BOOK: The Partial Fraction Expansion of the Cotangent</title>
       <link>/entries/Cotangent_PFD_Formula.html</link>
       <pubDate>Tue, 15 Mar 2022 00:00:00 +0000</pubDate>
       
       <guid>/entries/Cotangent_PFD_Formula.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>The Independence of the Continuum Hypothesis in Isabelle/ZF</title>
       <link>/entries/Independence_CH.html</link>
       <pubDate>Sun, 06 Mar 2022 00:00:00 +0000</pubDate>
       
       <guid>/entries/Independence_CH.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Transitive Models of Fragments of ZFC</title>
       <link>/entries/Transitive_Models.html</link>
       <pubDate>Thu, 03 Mar 2022 00:00:00 +0000</pubDate>
       
       <guid>/entries/Transitive_Models.html</guid>
       <description></description>
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     <item>
       <title>Residuated Transition Systems</title>
       <link>/entries/ResiduatedTransitionSystem.html</link>
       <pubDate>Mon, 28 Feb 2022 00:00:00 +0000</pubDate>
       
       <guid>/entries/ResiduatedTransitionSystem.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Universal Hash Families</title>
       <link>/entries/Universal_Hash_Families.html</link>
       <pubDate>Sun, 20 Feb 2022 00:00:00 +0000</pubDate>
       
       <guid>/entries/Universal_Hash_Families.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Wetzel&#39;s Problem and the Continuum Hypothesis</title>
       <link>/entries/Wetzels_Problem.html</link>
       <pubDate>Fri, 18 Feb 2022 00:00:00 +0000</pubDate>
       
       <guid>/entries/Wetzels_Problem.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>First-Order Query Evaluation</title>
       <link>/entries/Eval_FO.html</link>
       <pubDate>Tue, 15 Feb 2022 00:00:00 +0000</pubDate>
       
       <guid>/entries/Eval_FO.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Multi-Head Monitoring of Metric Dynamic Logic</title>
       <link>/entries/VYDRA_MDL.html</link>
       <pubDate>Sun, 13 Feb 2022 00:00:00 +0000</pubDate>
       
       <guid>/entries/VYDRA_MDL.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Enumeration of Equivalence Relations</title>
       <link>/entries/Equivalence_Relation_Enumeration.html</link>
       <pubDate>Fri, 04 Feb 2022 00:00:00 +0000</pubDate>
       
       <guid>/entries/Equivalence_Relation_Enumeration.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Duality of Linear Programming</title>
       <link>/entries/LP_Duality.html</link>
       <pubDate>Thu, 03 Feb 2022 00:00:00 +0000</pubDate>
       
       <guid>/entries/LP_Duality.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Quasi-Borel Spaces</title>
       <link>/entries/Quasi_Borel_Spaces.html</link>
       <pubDate>Thu, 03 Feb 2022 00:00:00 +0000</pubDate>
       
       <guid>/entries/Quasi_Borel_Spaces.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>First-Order Theory of Rewriting</title>
       <link>/entries/FO_Theory_Rewriting.html</link>
       <pubDate>Wed, 02 Feb 2022 00:00:00 +0000</pubDate>
       
       <guid>/entries/FO_Theory_Rewriting.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>A Sequent Calculus Prover for First-Order Logic with Functions</title>
       <link>/entries/FOL_Seq_Calc2.html</link>
       <pubDate>Mon, 31 Jan 2022 00:00:00 +0000</pubDate>
       
       <guid>/entries/FOL_Seq_Calc2.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Young&#39;s Inequality for Increasing Functions</title>
       <link>/entries/Youngs_Inequality.html</link>
       <pubDate>Mon, 31 Jan 2022 00:00:00 +0000</pubDate>
       
       <guid>/entries/Youngs_Inequality.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Interpolation Polynomials (in HOL-Algebra)</title>
       <link>/entries/Interpolation_Polynomials_HOL_Algebra.html</link>
       <pubDate>Sat, 29 Jan 2022 00:00:00 +0000</pubDate>
       
       <guid>/entries/Interpolation_Polynomials_HOL_Algebra.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Median Method</title>
       <link>/entries/Median_Method.html</link>
       <pubDate>Tue, 25 Jan 2022 00:00:00 +0000</pubDate>
       
       <guid>/entries/Median_Method.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Actuarial Mathematics</title>
       <link>/entries/Actuarial_Mathematics.html</link>
       <pubDate>Sun, 23 Jan 2022 00:00:00 +0000</pubDate>
       
       <guid>/entries/Actuarial_Mathematics.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Irrational numbers from THE BOOK</title>
       <link>/entries/Irrationals_From_THEBOOK.html</link>
       <pubDate>Sat, 08 Jan 2022 00:00:00 +0000</pubDate>
       
       <guid>/entries/Irrationals_From_THEBOOK.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Knight&#39;s Tour Revisited Revisited</title>
       <link>/entries/Knights_Tour.html</link>
       <pubDate>Tue, 04 Jan 2022 00:00:00 +0000</pubDate>
       
       <guid>/entries/Knights_Tour.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Hyperdual Numbers and Forward Differentiation</title>
       <link>/entries/Hyperdual.html</link>
       <pubDate>Fri, 31 Dec 2021 00:00:00 +0000</pubDate>
       
       <guid>/entries/Hyperdual.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Gale-Shapley Algorithm</title>
       <link>/entries/Gale_Shapley.html</link>
       <pubDate>Wed, 29 Dec 2021 00:00:00 +0000</pubDate>
       
       <guid>/entries/Gale_Shapley.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Roth&#39;s Theorem on Arithmetic Progressions</title>
       <link>/entries/Roth_Arithmetic_Progressions.html</link>
       <pubDate>Tue, 28 Dec 2021 00:00:00 +0000</pubDate>
       
       <guid>/entries/Roth_Arithmetic_Progressions.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Markov Decision Processes with Rewards</title>
       <link>/entries/MDP-Rewards.html</link>
       <pubDate>Thu, 16 Dec 2021 00:00:00 +0000</pubDate>
       
       <guid>/entries/MDP-Rewards.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Verified Algorithms for Solving Markov Decision Processes</title>
       <link>/entries/MDP-Algorithms.html</link>
       <pubDate>Thu, 16 Dec 2021 00:00:00 +0000</pubDate>
       
       <guid>/entries/MDP-Algorithms.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Regular Tree Relations</title>
       <link>/entries/Regular_Tree_Relations.html</link>
       <pubDate>Wed, 15 Dec 2021 00:00:00 +0000</pubDate>
       
       <guid>/entries/Regular_Tree_Relations.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Simplicial Complexes and Boolean functions</title>
       <link>/entries/Simplicial_complexes_and_boolean_functions.html</link>
       <pubDate>Mon, 29 Nov 2021 00:00:00 +0000</pubDate>
       
       <guid>/entries/Simplicial_complexes_and_boolean_functions.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>van Emde Boas Trees</title>
       <link>/entries/Van_Emde_Boas_Trees.html</link>
       <pubDate>Tue, 23 Nov 2021 00:00:00 +0000</pubDate>
       
       <guid>/entries/Van_Emde_Boas_Trees.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Foundation of geometry in planes, and some complements: Excluding the parallel axioms</title>
       <link>/entries/Foundation_of_geometry.html</link>
       <pubDate>Mon, 22 Nov 2021 00:00:00 +0000</pubDate>
       
       <guid>/entries/Foundation_of_geometry.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>The Hahn and Jordan Decomposition Theorems</title>
       <link>/entries/Hahn_Jordan_Decomposition.html</link>
       <pubDate>Fri, 19 Nov 2021 00:00:00 +0000</pubDate>
       
       <guid>/entries/Hahn_Jordan_Decomposition.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Automating Public Announcement Logic and the Wise Men Puzzle in Isabelle/HOL</title>
       <link>/entries/PAL.html</link>
       <pubDate>Mon, 08 Nov 2021 00:00:00 +0000</pubDate>
       
       <guid>/entries/PAL.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Exploring Simplified Variants of Gödel’s Ontological Argument in Isabelle/HOL</title>
       <link>/entries/SimplifiedOntologicalArgument.html</link>
       <pubDate>Mon, 08 Nov 2021 00:00:00 +0000</pubDate>
       
       <guid>/entries/SimplifiedOntologicalArgument.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Factorization of Polynomials with Algebraic Coefficients</title>
       <link>/entries/Factor_Algebraic_Polynomial.html</link>
       <pubDate>Mon, 08 Nov 2021 00:00:00 +0000</pubDate>
       
       <guid>/entries/Factor_Algebraic_Polynomial.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Real Exponents as the Limits of Sequences of Rational Exponents</title>
       <link>/entries/Real_Power.html</link>
       <pubDate>Mon, 08 Nov 2021 00:00:00 +0000</pubDate>
       
       <guid>/entries/Real_Power.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Szemerédi&#39;s Regularity Lemma</title>
       <link>/entries/Szemeredi_Regularity.html</link>
       <pubDate>Fri, 05 Nov 2021 00:00:00 +0000</pubDate>
       
       <guid>/entries/Szemeredi_Regularity.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Quantum and Classical Registers</title>
       <link>/entries/Registers.html</link>
       <pubDate>Thu, 28 Oct 2021 00:00:00 +0000</pubDate>
       
       <guid>/entries/Registers.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Belief Revision Theory</title>
       <link>/entries/Belief_Revision.html</link>
       <pubDate>Tue, 19 Oct 2021 00:00:00 +0000</pubDate>
       
       <guid>/entries/Belief_Revision.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>X86 instruction semantics and basic block symbolic execution</title>
       <link>/entries/X86_Semantics.html</link>
       <pubDate>Wed, 13 Oct 2021 00:00:00 +0000</pubDate>
       
       <guid>/entries/X86_Semantics.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Algebras for Iteration, Infinite Executions and Correctness of Sequential Computations</title>
       <link>/entries/Correctness_Algebras.html</link>
       <pubDate>Tue, 12 Oct 2021 00:00:00 +0000</pubDate>
       
       <guid>/entries/Correctness_Algebras.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Verified Quadratic Virtual Substitution for Real Arithmetic</title>
       <link>/entries/Virtual_Substitution.html</link>
       <pubDate>Sat, 02 Oct 2021 00:00:00 +0000</pubDate>
       
       <guid>/entries/Virtual_Substitution.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Soundness and Completeness of an Axiomatic System for First-Order Logic</title>
       <link>/entries/FOL_Axiomatic.html</link>
       <pubDate>Fri, 24 Sep 2021 00:00:00 +0000</pubDate>
       
       <guid>/entries/FOL_Axiomatic.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Complex Bounded Operators</title>
       <link>/entries/Complex_Bounded_Operators.html</link>
       <pubDate>Sat, 18 Sep 2021 00:00:00 +0000</pubDate>
       
       <guid>/entries/Complex_Bounded_Operators.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>A Formalization of Weighted Path Orders and Recursive Path Orders</title>
       <link>/entries/Weighted_Path_Order.html</link>
       <pubDate>Thu, 16 Sep 2021 00:00:00 +0000</pubDate>
       
       <guid>/entries/Weighted_Path_Order.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Category Theory for ZFC in HOL I: Foundations: Design Patterns, Set Theory, Digraphs, Semicategories</title>
       <link>/entries/CZH_Foundations.html</link>
       <pubDate>Mon, 06 Sep 2021 00:00:00 +0000</pubDate>
       
       <guid>/entries/CZH_Foundations.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Category Theory for ZFC in HOL II: Elementary Theory of 1-Categories</title>
       <link>/entries/CZH_Elementary_Categories.html</link>
       <pubDate>Mon, 06 Sep 2021 00:00:00 +0000</pubDate>
       
       <guid>/entries/CZH_Elementary_Categories.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Category Theory for ZFC in HOL III: Universal Constructions</title>
       <link>/entries/CZH_Universal_Constructions.html</link>
       <pubDate>Mon, 06 Sep 2021 00:00:00 +0000</pubDate>
       
       <guid>/entries/CZH_Universal_Constructions.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Conditional Simplification</title>
       <link>/entries/Conditional_Simplification.html</link>
       <pubDate>Mon, 06 Sep 2021 00:00:00 +0000</pubDate>
       
       <guid>/entries/Conditional_Simplification.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Conditional Transfer Rule</title>
       <link>/entries/Conditional_Transfer_Rule.html</link>
       <pubDate>Mon, 06 Sep 2021 00:00:00 +0000</pubDate>
       
       <guid>/entries/Conditional_Transfer_Rule.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Extension of Types-To-Sets</title>
       <link>/entries/Types_To_Sets_Extension.html</link>
       <pubDate>Mon, 06 Sep 2021 00:00:00 +0000</pubDate>
       
       <guid>/entries/Types_To_Sets_Extension.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>IDE: Introduction, Destruction, Elimination</title>
       <link>/entries/Intro_Dest_Elim.html</link>
       <pubDate>Mon, 06 Sep 2021 00:00:00 +0000</pubDate>
       
       <guid>/entries/Intro_Dest_Elim.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>A data flow analysis algorithm for computing dominators</title>
       <link>/entries/Dominance_CHK.html</link>
       <pubDate>Sun, 05 Sep 2021 00:00:00 +0000</pubDate>
       
       <guid>/entries/Dominance_CHK.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Solving Cubic and Quartic Equations</title>
       <link>/entries/Cubic_Quartic_Equations.html</link>
       <pubDate>Fri, 03 Sep 2021 00:00:00 +0000</pubDate>
       
       <guid>/entries/Cubic_Quartic_Equations.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Logging-independent Message Anonymity in the Relational Method</title>
       <link>/entries/Logging_Independent_Anonymity.html</link>
       <pubDate>Thu, 26 Aug 2021 00:00:00 +0000</pubDate>
       
       <guid>/entries/Logging_Independent_Anonymity.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>The Theorem of Three Circles</title>
       <link>/entries/Three_Circles.html</link>
       <pubDate>Sat, 21 Aug 2021 00:00:00 +0000</pubDate>
       
       <guid>/entries/Three_Circles.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>CoCon: A Confidentiality-Verified Conference Management System</title>
       <link>/entries/CoCon.html</link>
       <pubDate>Mon, 16 Aug 2021 00:00:00 +0000</pubDate>
       
       <guid>/entries/CoCon.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Compositional BD Security</title>
       <link>/entries/BD_Security_Compositional.html</link>
       <pubDate>Mon, 16 Aug 2021 00:00:00 +0000</pubDate>
       
       <guid>/entries/BD_Security_Compositional.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>CoSMed: A confidentiality-verified social media platform</title>
       <link>/entries/CoSMed.html</link>
       <pubDate>Mon, 16 Aug 2021 00:00:00 +0000</pubDate>
       
       <guid>/entries/CoSMed.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>CoSMeDis: A confidentiality-verified distributed social media platform</title>
       <link>/entries/CoSMeDis.html</link>
       <pubDate>Mon, 16 Aug 2021 00:00:00 +0000</pubDate>
       
       <guid>/entries/CoSMeDis.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Fresh identifiers</title>
       <link>/entries/Fresh_Identifiers.html</link>
       <pubDate>Mon, 16 Aug 2021 00:00:00 +0000</pubDate>
       
       <guid>/entries/Fresh_Identifiers.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Combinatorial Design Theory</title>
       <link>/entries/Design_Theory.html</link>
       <pubDate>Fri, 13 Aug 2021 00:00:00 +0000</pubDate>
       
       <guid>/entries/Design_Theory.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Relational Forests</title>
       <link>/entries/Relational_Forests.html</link>
       <pubDate>Tue, 03 Aug 2021 00:00:00 +0000</pubDate>
       
       <guid>/entries/Relational_Forests.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Schutz&#39; Independent Axioms for Minkowski Spacetime</title>
       <link>/entries/Schutz_Spacetime.html</link>
       <pubDate>Tue, 27 Jul 2021 00:00:00 +0000</pubDate>
       
       <guid>/entries/Schutz_Spacetime.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Finitely Generated Abelian Groups</title>
       <link>/entries/Finitely_Generated_Abelian_Groups.html</link>
       <pubDate>Wed, 07 Jul 2021 00:00:00 +0000</pubDate>
       
       <guid>/entries/Finitely_Generated_Abelian_Groups.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>SpecCheck - Specification-Based Testing for Isabelle/ML</title>
       <link>/entries/SpecCheck.html</link>
       <pubDate>Thu, 01 Jul 2021 00:00:00 +0000</pubDate>
       
       <guid>/entries/SpecCheck.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Van der Waerden&#39;s Theorem</title>
       <link>/entries/Van_der_Waerden.html</link>
       <pubDate>Tue, 22 Jun 2021 00:00:00 +0000</pubDate>
       
       <guid>/entries/Van_der_Waerden.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>MiniSail - A kernel language for the ISA specification language SAIL</title>
       <link>/entries/MiniSail.html</link>
       <pubDate>Fri, 18 Jun 2021 00:00:00 +0000</pubDate>
       
       <guid>/entries/MiniSail.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Public Announcement Logic</title>
       <link>/entries/Public_Announcement_Logic.html</link>
       <pubDate>Thu, 17 Jun 2021 00:00:00 +0000</pubDate>
       
       <guid>/entries/Public_Announcement_Logic.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>A Shorter Compiler Correctness Proof for Language IMP</title>
       <link>/entries/IMP_Compiler.html</link>
       <pubDate>Fri, 04 Jun 2021 00:00:00 +0000</pubDate>
       
       <guid>/entries/IMP_Compiler.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Combinatorics on Words Basics</title>
       <link>/entries/Combinatorics_Words.html</link>
       <pubDate>Mon, 24 May 2021 00:00:00 +0000</pubDate>
       
       <guid>/entries/Combinatorics_Words.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Graph Lemma</title>
       <link>/entries/Combinatorics_Words_Graph_Lemma.html</link>
       <pubDate>Mon, 24 May 2021 00:00:00 +0000</pubDate>
       
       <guid>/entries/Combinatorics_Words_Graph_Lemma.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Lyndon words</title>
       <link>/entries/Combinatorics_Words_Lyndon.html</link>
       <pubDate>Mon, 24 May 2021 00:00:00 +0000</pubDate>
       
       <guid>/entries/Combinatorics_Words_Lyndon.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Regression Test Selection</title>
       <link>/entries/Regression_Test_Selection.html</link>
       <pubDate>Fri, 30 Apr 2021 00:00:00 +0000</pubDate>
       
       <guid>/entries/Regression_Test_Selection.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Isabelle&#39;s Metalogic: Formalization and Proof Checker</title>
       <link>/entries/Metalogic_ProofChecker.html</link>
       <pubDate>Tue, 27 Apr 2021 00:00:00 +0000</pubDate>
       
       <guid>/entries/Metalogic_ProofChecker.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Lifting the Exponent</title>
       <link>/entries/Lifting_the_Exponent.html</link>
       <pubDate>Tue, 27 Apr 2021 00:00:00 +0000</pubDate>
       
       <guid>/entries/Lifting_the_Exponent.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>The BKR Decision Procedure for Univariate Real Arithmetic</title>
       <link>/entries/BenOr_Kozen_Reif.html</link>
       <pubDate>Sat, 24 Apr 2021 00:00:00 +0000</pubDate>
       
       <guid>/entries/BenOr_Kozen_Reif.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Gale-Stewart Games</title>
       <link>/entries/GaleStewart_Games.html</link>
       <pubDate>Fri, 23 Apr 2021 00:00:00 +0000</pubDate>
       
       <guid>/entries/GaleStewart_Games.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Formalization of Timely Dataflow&#39;s Progress Tracking Protocol</title>
       <link>/entries/Progress_Tracking.html</link>
       <pubDate>Tue, 13 Apr 2021 00:00:00 +0000</pubDate>
       
       <guid>/entries/Progress_Tracking.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Information Flow Control via Dependency Tracking</title>
       <link>/entries/IFC_Tracking.html</link>
       <pubDate>Thu, 01 Apr 2021 00:00:00 +0000</pubDate>
       
       <guid>/entries/IFC_Tracking.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Grothendieck&#39;s Schemes in Algebraic Geometry</title>
       <link>/entries/Grothendieck_Schemes.html</link>
       <pubDate>Mon, 29 Mar 2021 00:00:00 +0000</pubDate>
       
       <guid>/entries/Grothendieck_Schemes.html</guid>
       <description></description>
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     <item>
       <title>Hensel&#39;s Lemma for the p-adic Integers</title>
       <link>/entries/Padic_Ints.html</link>
       <pubDate>Tue, 23 Mar 2021 00:00:00 +0000</pubDate>
       
       <guid>/entries/Padic_Ints.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Constructive Cryptography in HOL: the Communication Modeling Aspect</title>
       <link>/entries/Constructive_Cryptography_CM.html</link>
       <pubDate>Wed, 17 Mar 2021 00:00:00 +0000</pubDate>
       
       <guid>/entries/Constructive_Cryptography_CM.html</guid>
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     <item>
       <title>Two algorithms based on modular arithmetic: lattice basis reduction and Hermite normal form computation</title>
       <link>/entries/Modular_arithmetic_LLL_and_HNF_algorithms.html</link>
       <pubDate>Fri, 12 Mar 2021 00:00:00 +0000</pubDate>
       
       <guid>/entries/Modular_arithmetic_LLL_and_HNF_algorithms.html</guid>
       <description></description>
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     <item>
       <title>Quantum projective measurements and the CHSH inequality</title>
       <link>/entries/Projective_Measurements.html</link>
       <pubDate>Wed, 03 Mar 2021 00:00:00 +0000</pubDate>
       
       <guid>/entries/Projective_Measurements.html</guid>
       <description></description>
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     <item>
       <title>The Hermite–Lindemann–Weierstraß Transcendence Theorem</title>
       <link>/entries/Hermite_Lindemann.html</link>
       <pubDate>Wed, 03 Mar 2021 00:00:00 +0000</pubDate>
       
       <guid>/entries/Hermite_Lindemann.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Mereology</title>
       <link>/entries/Mereology.html</link>
       <pubDate>Mon, 01 Mar 2021 00:00:00 +0000</pubDate>
       
       <guid>/entries/Mereology.html</guid>
       <description></description>
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     <item>
       <title>The Sunflower Lemma of Erdős and Rado</title>
       <link>/entries/Sunflowers.html</link>
       <pubDate>Thu, 25 Feb 2021 00:00:00 +0000</pubDate>
       
       <guid>/entries/Sunflowers.html</guid>
       <description></description>
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     <item>
       <title>A Verified Imperative Implementation of B-Trees</title>
       <link>/entries/BTree.html</link>
       <pubDate>Wed, 24 Feb 2021 00:00:00 +0000</pubDate>
       
       <guid>/entries/BTree.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Formal Puiseux Series</title>
       <link>/entries/Formal_Puiseux_Series.html</link>
       <pubDate>Wed, 17 Feb 2021 00:00:00 +0000</pubDate>
       
       <guid>/entries/Formal_Puiseux_Series.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>The Laws of Large Numbers</title>
       <link>/entries/Laws_of_Large_Numbers.html</link>
       <pubDate>Wed, 10 Feb 2021 00:00:00 +0000</pubDate>
       
       <guid>/entries/Laws_of_Large_Numbers.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Tarski&#39;s Parallel Postulate implies the 5th Postulate of Euclid, the Postulate of Playfair and the original Parallel Postulate of Euclid</title>
       <link>/entries/IsaGeoCoq.html</link>
       <pubDate>Sun, 31 Jan 2021 00:00:00 +0000</pubDate>
       
       <guid>/entries/IsaGeoCoq.html</guid>
       <description></description>
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     <item>
       <title>Solution to the xkcd Blue Eyes puzzle</title>
       <link>/entries/Blue_Eyes.html</link>
       <pubDate>Sat, 30 Jan 2021 00:00:00 +0000</pubDate>
       
       <guid>/entries/Blue_Eyes.html</guid>
       <description></description>
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     <item>
       <title>Hood-Melville Queue</title>
       <link>/entries/Hood_Melville_Queue.html</link>
       <pubDate>Mon, 18 Jan 2021 00:00:00 +0000</pubDate>
       
       <guid>/entries/Hood_Melville_Queue.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>JinjaDCI: a Java semantics with dynamic class initialization</title>
       <link>/entries/JinjaDCI.html</link>
       <pubDate>Mon, 11 Jan 2021 00:00:00 +0000</pubDate>
       
       <guid>/entries/JinjaDCI.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Cofinality and the Delta System Lemma</title>
       <link>/entries/Delta_System_Lemma.html</link>
       <pubDate>Sun, 27 Dec 2020 00:00:00 +0000</pubDate>
       
       <guid>/entries/Delta_System_Lemma.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Topological semantics for paraconsistent and paracomplete logics</title>
       <link>/entries/Topological_Semantics.html</link>
       <pubDate>Thu, 17 Dec 2020 00:00:00 +0000</pubDate>
       
       <guid>/entries/Topological_Semantics.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Relational Minimum Spanning Tree Algorithms</title>
       <link>/entries/Relational_Minimum_Spanning_Trees.html</link>
       <pubDate>Tue, 08 Dec 2020 00:00:00 +0000</pubDate>
       
       <guid>/entries/Relational_Minimum_Spanning_Trees.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Inline Caching and Unboxing Optimization for Interpreters</title>
       <link>/entries/Interpreter_Optimizations.html</link>
       <pubDate>Mon, 07 Dec 2020 00:00:00 +0000</pubDate>
       
       <guid>/entries/Interpreter_Optimizations.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>The Relational Method with Message Anonymity for the Verification of Cryptographic Protocols</title>
       <link>/entries/Relational_Method.html</link>
       <pubDate>Sat, 05 Dec 2020 00:00:00 +0000</pubDate>
       
       <guid>/entries/Relational_Method.html</guid>
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     </item>
     
     <item>
       <title>Isabelle Marries Dirac: a Library for Quantum Computation and Quantum Information</title>
       <link>/entries/Isabelle_Marries_Dirac.html</link>
       <pubDate>Sun, 22 Nov 2020 00:00:00 +0000</pubDate>
       
       <guid>/entries/Isabelle_Marries_Dirac.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>The HOL-CSP Refinement Toolkit</title>
       <link>/entries/CSP_RefTK.html</link>
       <pubDate>Thu, 19 Nov 2020 00:00:00 +0000</pubDate>
       
       <guid>/entries/CSP_RefTK.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>AI Planning Languages Semantics</title>
       <link>/entries/AI_Planning_Languages_Semantics.html</link>
       <pubDate>Thu, 29 Oct 2020 00:00:00 +0000</pubDate>
       
       <guid>/entries/AI_Planning_Languages_Semantics.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Verified SAT-Based AI Planning</title>
       <link>/entries/Verified_SAT_Based_AI_Planning.html</link>
       <pubDate>Thu, 29 Oct 2020 00:00:00 +0000</pubDate>
       
       <guid>/entries/Verified_SAT_Based_AI_Planning.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>A Sound Type System for Physical Quantities, Units, and Measurements</title>
       <link>/entries/Physical_Quantities.html</link>
       <pubDate>Tue, 20 Oct 2020 00:00:00 +0000</pubDate>
       
       <guid>/entries/Physical_Quantities.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Finite Map Extras</title>
       <link>/entries/Finite-Map-Extras.html</link>
       <pubDate>Mon, 12 Oct 2020 00:00:00 +0000</pubDate>
       
       <guid>/entries/Finite-Map-Extras.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>A Formal Model of the Document Object Model with Shadow Roots</title>
       <link>/entries/Shadow_DOM.html</link>
       <pubDate>Mon, 28 Sep 2020 00:00:00 +0000</pubDate>
       
       <guid>/entries/Shadow_DOM.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>A Formal Model of the Safely Composable Document Object Model with Shadow Roots</title>
       <link>/entries/Shadow_SC_DOM.html</link>
       <pubDate>Mon, 28 Sep 2020 00:00:00 +0000</pubDate>
       
       <guid>/entries/Shadow_SC_DOM.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>A Formalization of Safely Composable Web Components</title>
       <link>/entries/SC_DOM_Components.html</link>
       <pubDate>Mon, 28 Sep 2020 00:00:00 +0000</pubDate>
       
       <guid>/entries/SC_DOM_Components.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>A Formalization of Web Components</title>
       <link>/entries/DOM_Components.html</link>
       <pubDate>Mon, 28 Sep 2020 00:00:00 +0000</pubDate>
       
       <guid>/entries/DOM_Components.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>The Safely Composable DOM</title>
       <link>/entries/Core_SC_DOM.html</link>
       <pubDate>Mon, 28 Sep 2020 00:00:00 +0000</pubDate>
       
       <guid>/entries/Core_SC_DOM.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>An Abstract Formalization of G&amp;ouml;del&#39;s Incompleteness Theorems</title>
       <link>/entries/Goedel_Incompleteness.html</link>
       <pubDate>Wed, 16 Sep 2020 00:00:00 +0000</pubDate>
       
       <guid>/entries/Goedel_Incompleteness.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>From Abstract to Concrete G&amp;ouml;del&#39;s Incompleteness Theorems&amp;mdash;Part I</title>
       <link>/entries/Goedel_HFSet_Semantic.html</link>
       <pubDate>Wed, 16 Sep 2020 00:00:00 +0000</pubDate>
       
       <guid>/entries/Goedel_HFSet_Semantic.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>From Abstract to Concrete G&amp;ouml;del&#39;s Incompleteness Theorems&amp;mdash;Part II</title>
       <link>/entries/Goedel_HFSet_Semanticless.html</link>
       <pubDate>Wed, 16 Sep 2020 00:00:00 +0000</pubDate>
       
       <guid>/entries/Goedel_HFSet_Semanticless.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Robinson Arithmetic</title>
       <link>/entries/Robinson_Arithmetic.html</link>
       <pubDate>Wed, 16 Sep 2020 00:00:00 +0000</pubDate>
       
       <guid>/entries/Robinson_Arithmetic.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Syntax-Independent Logic Infrastructure</title>
       <link>/entries/Syntax_Independent_Logic.html</link>
       <pubDate>Wed, 16 Sep 2020 00:00:00 +0000</pubDate>
       
       <guid>/entries/Syntax_Independent_Logic.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>A Formal Model of Extended Finite State Machines</title>
       <link>/entries/Extended_Finite_State_Machines.html</link>
       <pubDate>Mon, 07 Sep 2020 00:00:00 +0000</pubDate>
       
       <guid>/entries/Extended_Finite_State_Machines.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Inference of Extended Finite State Machines</title>
       <link>/entries/Extended_Finite_State_Machine_Inference.html</link>
       <pubDate>Mon, 07 Sep 2020 00:00:00 +0000</pubDate>
       
       <guid>/entries/Extended_Finite_State_Machine_Inference.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Practical Algebraic Calculus Checker</title>
       <link>/entries/PAC_Checker.html</link>
       <pubDate>Mon, 31 Aug 2020 00:00:00 +0000</pubDate>
       
       <guid>/entries/PAC_Checker.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Some classical results in inductive inference of recursive functions</title>
       <link>/entries/Inductive_Inference.html</link>
       <pubDate>Mon, 31 Aug 2020 00:00:00 +0000</pubDate>
       
       <guid>/entries/Inductive_Inference.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Relational Disjoint-Set Forests</title>
       <link>/entries/Relational_Disjoint_Set_Forests.html</link>
       <pubDate>Wed, 26 Aug 2020 00:00:00 +0000</pubDate>
       
       <guid>/entries/Relational_Disjoint_Set_Forests.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Extensions to the Comprehensive Framework for Saturation Theorem Proving</title>
       <link>/entries/Saturation_Framework_Extensions.html</link>
       <pubDate>Tue, 25 Aug 2020 00:00:00 +0000</pubDate>
       
       <guid>/entries/Saturation_Framework_Extensions.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Putting the `K&#39; into Bird&#39;s derivation of Knuth-Morris-Pratt string matching</title>
       <link>/entries/BirdKMP.html</link>
       <pubDate>Tue, 25 Aug 2020 00:00:00 +0000</pubDate>
       
       <guid>/entries/BirdKMP.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Amicable Numbers</title>
       <link>/entries/Amicable_Numbers.html</link>
       <pubDate>Tue, 04 Aug 2020 00:00:00 +0000</pubDate>
       
       <guid>/entries/Amicable_Numbers.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Ordinal Partitions</title>
       <link>/entries/Ordinal_Partitions.html</link>
       <pubDate>Mon, 03 Aug 2020 00:00:00 +0000</pubDate>
       
       <guid>/entries/Ordinal_Partitions.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>A Formal Proof of The Chandy--Lamport Distributed Snapshot Algorithm</title>
       <link>/entries/Chandy_Lamport.html</link>
       <pubDate>Tue, 21 Jul 2020 00:00:00 +0000</pubDate>
       
       <guid>/entries/Chandy_Lamport.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Relational Characterisations of Paths</title>
       <link>/entries/Relational_Paths.html</link>
       <pubDate>Mon, 13 Jul 2020 00:00:00 +0000</pubDate>
       
       <guid>/entries/Relational_Paths.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>A Formally Verified Checker of the Safe Distance Traffic Rules for Autonomous Vehicles</title>
       <link>/entries/Safe_Distance.html</link>
       <pubDate>Mon, 01 Jun 2020 00:00:00 +0000</pubDate>
       
       <guid>/entries/Safe_Distance.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>A verified algorithm for computing the Smith normal form of a matrix</title>
       <link>/entries/Smith_Normal_Form.html</link>
       <pubDate>Sat, 23 May 2020 00:00:00 +0000</pubDate>
       
       <guid>/entries/Smith_Normal_Form.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>The Nash-Williams Partition Theorem</title>
       <link>/entries/Nash_Williams.html</link>
       <pubDate>Sat, 16 May 2020 00:00:00 +0000</pubDate>
       
       <guid>/entries/Nash_Williams.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>A Formalization of Knuth–Bendix Orders</title>
       <link>/entries/Knuth_Bendix_Order.html</link>
       <pubDate>Wed, 13 May 2020 00:00:00 +0000</pubDate>
       
       <guid>/entries/Knuth_Bendix_Order.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Irrationality Criteria for Series by Erdős and Straus</title>
       <link>/entries/Irrational_Series_Erdos_Straus.html</link>
       <pubDate>Tue, 12 May 2020 00:00:00 +0000</pubDate>
       
       <guid>/entries/Irrational_Series_Erdos_Straus.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Recursion Theorem in ZF</title>
       <link>/entries/Recursion-Addition.html</link>
       <pubDate>Mon, 11 May 2020 00:00:00 +0000</pubDate>
       
       <guid>/entries/Recursion-Addition.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>An Efficient Normalisation Procedure for Linear Temporal Logic: Isabelle/HOL Formalisation</title>
       <link>/entries/LTL_Normal_Form.html</link>
       <pubDate>Fri, 08 May 2020 00:00:00 +0000</pubDate>
       
       <guid>/entries/LTL_Normal_Form.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Formalization of Forcing in Isabelle/ZF</title>
       <link>/entries/Forcing.html</link>
       <pubDate>Wed, 06 May 2020 00:00:00 +0000</pubDate>
       
       <guid>/entries/Forcing.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Banach-Steinhaus Theorem</title>
       <link>/entries/Banach_Steinhaus.html</link>
       <pubDate>Sat, 02 May 2020 00:00:00 +0000</pubDate>
       
       <guid>/entries/Banach_Steinhaus.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Attack Trees in Isabelle for GDPR compliance of IoT healthcare systems</title>
       <link>/entries/Attack_Trees.html</link>
       <pubDate>Mon, 27 Apr 2020 00:00:00 +0000</pubDate>
       
       <guid>/entries/Attack_Trees.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Gaussian Integers</title>
       <link>/entries/Gaussian_Integers.html</link>
       <pubDate>Fri, 24 Apr 2020 00:00:00 +0000</pubDate>
       
       <guid>/entries/Gaussian_Integers.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Power Sum Polynomials</title>
       <link>/entries/Power_Sum_Polynomials.html</link>
       <pubDate>Fri, 24 Apr 2020 00:00:00 +0000</pubDate>
       
       <guid>/entries/Power_Sum_Polynomials.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>The Lambert W Function on the Reals</title>
       <link>/entries/Lambert_W.html</link>
       <pubDate>Fri, 24 Apr 2020 00:00:00 +0000</pubDate>
       
       <guid>/entries/Lambert_W.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Matrices for ODEs</title>
       <link>/entries/Matrices_for_ODEs.html</link>
       <pubDate>Sun, 19 Apr 2020 00:00:00 +0000</pubDate>
       
       <guid>/entries/Matrices_for_ODEs.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Authenticated Data Structures As Functors</title>
       <link>/entries/ADS_Functor.html</link>
       <pubDate>Thu, 16 Apr 2020 00:00:00 +0000</pubDate>
       
       <guid>/entries/ADS_Functor.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Formalization of an Algorithm for Greedily Computing Associative Aggregations on Sliding Windows</title>
       <link>/entries/Sliding_Window_Algorithm.html</link>
       <pubDate>Fri, 10 Apr 2020 00:00:00 +0000</pubDate>
       
       <guid>/entries/Sliding_Window_Algorithm.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>A Comprehensive Framework for Saturation Theorem Proving</title>
       <link>/entries/Saturation_Framework.html</link>
       <pubDate>Thu, 09 Apr 2020 00:00:00 +0000</pubDate>
       
       <guid>/entries/Saturation_Framework.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Formalization of an Optimized Monitoring Algorithm for Metric First-Order Dynamic Logic with Aggregations</title>
       <link>/entries/MFODL_Monitor_Optimized.html</link>
       <pubDate>Thu, 09 Apr 2020 00:00:00 +0000</pubDate>
       
       <guid>/entries/MFODL_Monitor_Optimized.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Automated Stateful Protocol Verification</title>
       <link>/entries/Automated_Stateful_Protocol_Verification.html</link>
       <pubDate>Wed, 08 Apr 2020 00:00:00 +0000</pubDate>
       
       <guid>/entries/Automated_Stateful_Protocol_Verification.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Stateful Protocol Composition and Typing</title>
       <link>/entries/Stateful_Protocol_Composition_and_Typing.html</link>
       <pubDate>Wed, 08 Apr 2020 00:00:00 +0000</pubDate>
       
       <guid>/entries/Stateful_Protocol_Composition_and_Typing.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Lucas&#39;s Theorem</title>
       <link>/entries/Lucas_Theorem.html</link>
       <pubDate>Tue, 07 Apr 2020 00:00:00 +0000</pubDate>
       
       <guid>/entries/Lucas_Theorem.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Strong Eventual Consistency of the Collaborative Editing Framework WOOT</title>
       <link>/entries/WOOT_Strong_Eventual_Consistency.html</link>
       <pubDate>Wed, 25 Mar 2020 00:00:00 +0000</pubDate>
       
       <guid>/entries/WOOT_Strong_Eventual_Consistency.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Furstenberg&#39;s topology and his proof of the infinitude of primes</title>
       <link>/entries/Furstenberg_Topology.html</link>
       <pubDate>Sun, 22 Mar 2020 00:00:00 +0000</pubDate>
       
       <guid>/entries/Furstenberg_Topology.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>An Under-Approximate Relational Logic</title>
       <link>/entries/Relational-Incorrectness-Logic.html</link>
       <pubDate>Thu, 12 Mar 2020 00:00:00 +0000</pubDate>
       
       <guid>/entries/Relational-Incorrectness-Logic.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Hello World</title>
       <link>/entries/Hello_World.html</link>
       <pubDate>Sat, 07 Mar 2020 00:00:00 +0000</pubDate>
       
       <guid>/entries/Hello_World.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Implementing the Goodstein Function in &amp;lambda;-Calculus</title>
       <link>/entries/Goodstein_Lambda.html</link>
       <pubDate>Fri, 21 Feb 2020 00:00:00 +0000</pubDate>
       
       <guid>/entries/Goodstein_Lambda.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>A Generic Framework for Verified Compilers</title>
       <link>/entries/VeriComp.html</link>
       <pubDate>Mon, 10 Feb 2020 00:00:00 +0000</pubDate>
       
       <guid>/entries/VeriComp.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Arithmetic progressions and relative primes</title>
       <link>/entries/Arith_Prog_Rel_Primes.html</link>
       <pubDate>Sat, 01 Feb 2020 00:00:00 +0000</pubDate>
       
       <guid>/entries/Arith_Prog_Rel_Primes.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>A Hierarchy of Algebras for Boolean Subsets</title>
       <link>/entries/Subset_Boolean_Algebras.html</link>
       <pubDate>Fri, 31 Jan 2020 00:00:00 +0000</pubDate>
       
       <guid>/entries/Subset_Boolean_Algebras.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Mersenne primes and the Lucas–Lehmer test</title>
       <link>/entries/Mersenne_Primes.html</link>
       <pubDate>Fri, 17 Jan 2020 00:00:00 +0000</pubDate>
       
       <guid>/entries/Mersenne_Primes.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Verified Approximation Algorithms</title>
       <link>/entries/Approximation_Algorithms.html</link>
       <pubDate>Thu, 16 Jan 2020 00:00:00 +0000</pubDate>
       
       <guid>/entries/Approximation_Algorithms.html</guid>
       <description></description>
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       <title>Closest Pair of Points Algorithms</title>
       <link>/entries/Closest_Pair_Points.html</link>
       <pubDate>Mon, 13 Jan 2020 00:00:00 +0000</pubDate>
       
       <guid>/entries/Closest_Pair_Points.html</guid>
       <description></description>
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     <item>
       <title>Skip Lists</title>
       <link>/entries/Skip_Lists.html</link>
       <pubDate>Thu, 09 Jan 2020 00:00:00 +0000</pubDate>
       
       <guid>/entries/Skip_Lists.html</guid>
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       <title>Bicategories</title>
       <link>/entries/Bicategory.html</link>
       <pubDate>Mon, 06 Jan 2020 00:00:00 +0000</pubDate>
       
       <guid>/entries/Bicategory.html</guid>
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       <title>The Irrationality of ζ(3)</title>
       <link>/entries/Zeta_3_Irrational.html</link>
       <pubDate>Fri, 27 Dec 2019 00:00:00 +0000</pubDate>
       
       <guid>/entries/Zeta_3_Irrational.html</guid>
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     <item>
       <title>Formalizing a Seligman-Style Tableau System for Hybrid Logic</title>
       <link>/entries/Hybrid_Logic.html</link>
       <pubDate>Fri, 20 Dec 2019 00:00:00 +0000</pubDate>
       
       <guid>/entries/Hybrid_Logic.html</guid>
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     <item>
       <title>The Poincaré-Bendixson Theorem</title>
       <link>/entries/Poincare_Bendixson.html</link>
       <pubDate>Wed, 18 Dec 2019 00:00:00 +0000</pubDate>
       
       <guid>/entries/Poincare_Bendixson.html</guid>
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     <item>
       <title>Complex Geometry</title>
       <link>/entries/Complex_Geometry.html</link>
       <pubDate>Mon, 16 Dec 2019 00:00:00 +0000</pubDate>
       
       <guid>/entries/Complex_Geometry.html</guid>
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       <title>Poincaré Disc Model</title>
       <link>/entries/Poincare_Disc.html</link>
       <pubDate>Mon, 16 Dec 2019 00:00:00 +0000</pubDate>
       
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     <item>
       <title>Gauss Sums and the Pólya–Vinogradov Inequality</title>
       <link>/entries/Gauss_Sums.html</link>
       <pubDate>Tue, 10 Dec 2019 00:00:00 +0000</pubDate>
       
       <guid>/entries/Gauss_Sums.html</guid>
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     <item>
       <title>An Efficient Generalization of Counting Sort for Large, possibly Infinite Key Ranges</title>
       <link>/entries/Generalized_Counting_Sort.html</link>
       <pubDate>Wed, 04 Dec 2019 00:00:00 +0000</pubDate>
       
       <guid>/entries/Generalized_Counting_Sort.html</guid>
       <description></description>
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     <item>
       <title>Interval Arithmetic on 32-bit Words</title>
       <link>/entries/Interval_Arithmetic_Word32.html</link>
       <pubDate>Wed, 27 Nov 2019 00:00:00 +0000</pubDate>
       
       <guid>/entries/Interval_Arithmetic_Word32.html</guid>
       <description></description>
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     <item>
       <title>Zermelo Fraenkel Set Theory in Higher-Order Logic</title>
       <link>/entries/ZFC_in_HOL.html</link>
       <pubDate>Thu, 24 Oct 2019 00:00:00 +0000</pubDate>
       
       <guid>/entries/ZFC_in_HOL.html</guid>
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     <item>
       <title>Isabelle/C</title>
       <link>/entries/Isabelle_C.html</link>
       <pubDate>Tue, 22 Oct 2019 00:00:00 +0000</pubDate>
       
       <guid>/entries/Isabelle_C.html</guid>
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     <item>
       <title>VerifyThis 2019 -- Polished Isabelle Solutions</title>
       <link>/entries/VerifyThis2019.html</link>
       <pubDate>Wed, 16 Oct 2019 00:00:00 +0000</pubDate>
       
       <guid>/entries/VerifyThis2019.html</guid>
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     <item>
       <title>Aristotle&#39;s Assertoric Syllogistic</title>
       <link>/entries/Aristotles_Assertoric_Syllogistic.html</link>
       <pubDate>Tue, 08 Oct 2019 00:00:00 +0000</pubDate>
       
       <guid>/entries/Aristotles_Assertoric_Syllogistic.html</guid>
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     <item>
       <title>Sigma Protocols and Commitment Schemes</title>
       <link>/entries/Sigma_Commit_Crypto.html</link>
       <pubDate>Mon, 07 Oct 2019 00:00:00 +0000</pubDate>
       
       <guid>/entries/Sigma_Commit_Crypto.html</guid>
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     <item>
       <title>Clean - An Abstract Imperative Programming Language and its Theory</title>
       <link>/entries/Clean.html</link>
       <pubDate>Fri, 04 Oct 2019 00:00:00 +0000</pubDate>
       
       <guid>/entries/Clean.html</guid>
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     <item>
       <title>Formalization of Multiway-Join Algorithms</title>
       <link>/entries/Generic_Join.html</link>
       <pubDate>Mon, 16 Sep 2019 00:00:00 +0000</pubDate>
       
       <guid>/entries/Generic_Join.html</guid>
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     <item>
       <title>Verification Components for Hybrid Systems</title>
       <link>/entries/Hybrid_Systems_VCs.html</link>
       <pubDate>Tue, 10 Sep 2019 00:00:00 +0000</pubDate>
       
       <guid>/entries/Hybrid_Systems_VCs.html</guid>
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     <item>
       <title>Fourier Series</title>
       <link>/entries/Fourier.html</link>
       <pubDate>Fri, 06 Sep 2019 00:00:00 +0000</pubDate>
       
       <guid>/entries/Fourier.html</guid>
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     <item>
       <title>A Case Study in Basic Algebra</title>
       <link>/entries/Jacobson_Basic_Algebra.html</link>
       <pubDate>Fri, 30 Aug 2019 00:00:00 +0000</pubDate>
       
       <guid>/entries/Jacobson_Basic_Algebra.html</guid>
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     <item>
       <title>Formalisation of an Adaptive State Counting Algorithm</title>
       <link>/entries/Adaptive_State_Counting.html</link>
       <pubDate>Fri, 16 Aug 2019 00:00:00 +0000</pubDate>
       
       <guid>/entries/Adaptive_State_Counting.html</guid>
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     <item>
       <title>Laplace Transform</title>
       <link>/entries/Laplace_Transform.html</link>
       <pubDate>Wed, 14 Aug 2019 00:00:00 +0000</pubDate>
       
       <guid>/entries/Laplace_Transform.html</guid>
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     <item>
       <title>Communicating Concurrent Kleene Algebra for Distributed Systems Specification</title>
       <link>/entries/C2KA_DistributedSystems.html</link>
       <pubDate>Tue, 06 Aug 2019 00:00:00 +0000</pubDate>
       
       <guid>/entries/C2KA_DistributedSystems.html</guid>
       <description></description>
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     <item>
       <title>Linear Programming</title>
       <link>/entries/Linear_Programming.html</link>
       <pubDate>Tue, 06 Aug 2019 00:00:00 +0000</pubDate>
       
       <guid>/entries/Linear_Programming.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Selected Problems from the International Mathematical Olympiad 2019</title>
       <link>/entries/IMO2019.html</link>
       <pubDate>Mon, 05 Aug 2019 00:00:00 +0000</pubDate>
       
       <guid>/entries/IMO2019.html</guid>
       <description></description>
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     <item>
       <title>Stellar Quorum Systems</title>
       <link>/entries/Stellar_Quorums.html</link>
       <pubDate>Thu, 01 Aug 2019 00:00:00 +0000</pubDate>
       
       <guid>/entries/Stellar_Quorums.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>A Formal Development of a Polychronous Polytimed Coordination Language</title>
       <link>/entries/TESL_Language.html</link>
       <pubDate>Tue, 30 Jul 2019 00:00:00 +0000</pubDate>
       
       <guid>/entries/TESL_Language.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Order Extension and Szpilrajn&#39;s Extension Theorem</title>
       <link>/entries/Szpilrajn.html</link>
       <pubDate>Sat, 27 Jul 2019 00:00:00 +0000</pubDate>
       
       <guid>/entries/Szpilrajn.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>A Sequent Calculus for First-Order Logic</title>
       <link>/entries/FOL_Seq_Calc1.html</link>
       <pubDate>Thu, 18 Jul 2019 00:00:00 +0000</pubDate>
       
       <guid>/entries/FOL_Seq_Calc1.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>A Verified Code Generator from Isabelle/HOL to CakeML</title>
       <link>/entries/CakeML_Codegen.html</link>
       <pubDate>Mon, 08 Jul 2019 00:00:00 +0000</pubDate>
       
       <guid>/entries/CakeML_Codegen.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Formalization of a Monitoring Algorithm for Metric First-Order Temporal Logic</title>
       <link>/entries/MFOTL_Monitor.html</link>
       <pubDate>Thu, 04 Jul 2019 00:00:00 +0000</pubDate>
       
       <guid>/entries/MFOTL_Monitor.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Complete Non-Orders and Fixed Points</title>
       <link>/entries/Complete_Non_Orders.html</link>
       <pubDate>Thu, 27 Jun 2019 00:00:00 +0000</pubDate>
       
       <guid>/entries/Complete_Non_Orders.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Priority Search Trees</title>
       <link>/entries/Priority_Search_Trees.html</link>
       <pubDate>Tue, 25 Jun 2019 00:00:00 +0000</pubDate>
       
       <guid>/entries/Priority_Search_Trees.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Purely Functional, Simple, and Efficient Implementation of Prim and Dijkstra</title>
       <link>/entries/Prim_Dijkstra_Simple.html</link>
       <pubDate>Tue, 25 Jun 2019 00:00:00 +0000</pubDate>
       
       <guid>/entries/Prim_Dijkstra_Simple.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Linear Inequalities</title>
       <link>/entries/Linear_Inequalities.html</link>
       <pubDate>Fri, 21 Jun 2019 00:00:00 +0000</pubDate>
       
       <guid>/entries/Linear_Inequalities.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Hilbert&#39;s Nullstellensatz</title>
       <link>/entries/Nullstellensatz.html</link>
       <pubDate>Sun, 16 Jun 2019 00:00:00 +0000</pubDate>
       
       <guid>/entries/Nullstellensatz.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Gröbner Bases, Macaulay Matrices and Dubé&#39;s Degree Bounds</title>
       <link>/entries/Groebner_Macaulay.html</link>
       <pubDate>Sat, 15 Jun 2019 00:00:00 +0000</pubDate>
       
       <guid>/entries/Groebner_Macaulay.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Binary Heaps for IMP2</title>
       <link>/entries/IMP2_Binary_Heap.html</link>
       <pubDate>Thu, 13 Jun 2019 00:00:00 +0000</pubDate>
       
       <guid>/entries/IMP2_Binary_Heap.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Differential Game Logic</title>
       <link>/entries/Differential_Game_Logic.html</link>
       <pubDate>Mon, 03 Jun 2019 00:00:00 +0000</pubDate>
       
       <guid>/entries/Differential_Game_Logic.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Multidimensional Binary Search Trees</title>
       <link>/entries/KD_Tree.html</link>
       <pubDate>Thu, 30 May 2019 00:00:00 +0000</pubDate>
       
       <guid>/entries/KD_Tree.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Formalization of Generic Authenticated Data Structures</title>
       <link>/entries/LambdaAuth.html</link>
       <pubDate>Tue, 14 May 2019 00:00:00 +0000</pubDate>
       
       <guid>/entries/LambdaAuth.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Multi-Party Computation</title>
       <link>/entries/Multi_Party_Computation.html</link>
       <pubDate>Thu, 09 May 2019 00:00:00 +0000</pubDate>
       
       <guid>/entries/Multi_Party_Computation.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>HOL-CSP Version 2.0</title>
       <link>/entries/HOL-CSP.html</link>
       <pubDate>Fri, 26 Apr 2019 00:00:00 +0000</pubDate>
       
       <guid>/entries/HOL-CSP.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>A Compositional and Unified Translation of LTL into ω-Automata</title>
       <link>/entries/LTL_Master_Theorem.html</link>
       <pubDate>Tue, 16 Apr 2019 00:00:00 +0000</pubDate>
       
       <guid>/entries/LTL_Master_Theorem.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>A General Theory of Syntax with Bindings</title>
       <link>/entries/Binding_Syntax_Theory.html</link>
       <pubDate>Sat, 06 Apr 2019 00:00:00 +0000</pubDate>
       
       <guid>/entries/Binding_Syntax_Theory.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>The Transcendence of Certain Infinite Series</title>
       <link>/entries/Transcendence_Series_Hancl_Rucki.html</link>
       <pubDate>Wed, 27 Mar 2019 00:00:00 +0000</pubDate>
       
       <guid>/entries/Transcendence_Series_Hancl_Rucki.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Quantum Hoare Logic</title>
       <link>/entries/QHLProver.html</link>
       <pubDate>Sun, 24 Mar 2019 00:00:00 +0000</pubDate>
       
       <guid>/entries/QHLProver.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Safe OCL</title>
       <link>/entries/Safe_OCL.html</link>
       <pubDate>Sat, 09 Mar 2019 00:00:00 +0000</pubDate>
       
       <guid>/entries/Safe_OCL.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Elementary Facts About the Distribution of Primes</title>
       <link>/entries/Prime_Distribution_Elementary.html</link>
       <pubDate>Thu, 21 Feb 2019 00:00:00 +0000</pubDate>
       
       <guid>/entries/Prime_Distribution_Elementary.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Kruskal&#39;s Algorithm for Minimum Spanning Forest</title>
       <link>/entries/Kruskal.html</link>
       <pubDate>Thu, 14 Feb 2019 00:00:00 +0000</pubDate>
       
       <guid>/entries/Kruskal.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Probabilistic Primality Testing</title>
       <link>/entries/Probabilistic_Prime_Tests.html</link>
       <pubDate>Mon, 11 Feb 2019 00:00:00 +0000</pubDate>
       
       <guid>/entries/Probabilistic_Prime_Tests.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Universal Turing Machine</title>
       <link>/entries/Universal_Turing_Machine.html</link>
       <pubDate>Fri, 08 Feb 2019 00:00:00 +0000</pubDate>
       
       <guid>/entries/Universal_Turing_Machine.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Isabelle/UTP: Mechanised Theory Engineering for Unifying Theories of Programming</title>
       <link>/entries/UTP.html</link>
       <pubDate>Fri, 01 Feb 2019 00:00:00 +0000</pubDate>
       
       <guid>/entries/UTP.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>The Inversions of a List</title>
       <link>/entries/List_Inversions.html</link>
       <pubDate>Fri, 01 Feb 2019 00:00:00 +0000</pubDate>
       
       <guid>/entries/List_Inversions.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Farkas&#39; Lemma and Motzkin&#39;s Transposition Theorem</title>
       <link>/entries/Farkas.html</link>
       <pubDate>Thu, 17 Jan 2019 00:00:00 +0000</pubDate>
       
       <guid>/entries/Farkas.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>An Algebra for Higher-Order Terms</title>
       <link>/entries/Higher_Order_Terms.html</link>
       <pubDate>Tue, 15 Jan 2019 00:00:00 +0000</pubDate>
       
       <guid>/entries/Higher_Order_Terms.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>IMP2 – Simple Program Verification in Isabelle/HOL</title>
       <link>/entries/IMP2.html</link>
       <pubDate>Tue, 15 Jan 2019 00:00:00 +0000</pubDate>
       
       <guid>/entries/IMP2.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>A Reduction Theorem for Store Buffers</title>
       <link>/entries/Store_Buffer_Reduction.html</link>
       <pubDate>Mon, 07 Jan 2019 00:00:00 +0000</pubDate>
       
       <guid>/entries/Store_Buffer_Reduction.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>A Formal Model of the Document Object Model</title>
       <link>/entries/Core_DOM.html</link>
       <pubDate>Wed, 26 Dec 2018 00:00:00 +0000</pubDate>
       
       <guid>/entries/Core_DOM.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Formalization of Concurrent Revisions</title>
       <link>/entries/Concurrent_Revisions.html</link>
       <pubDate>Tue, 25 Dec 2018 00:00:00 +0000</pubDate>
       
       <guid>/entries/Concurrent_Revisions.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Verifying Imperative Programs using Auto2</title>
       <link>/entries/Auto2_Imperative_HOL.html</link>
       <pubDate>Fri, 21 Dec 2018 00:00:00 +0000</pubDate>
       
       <guid>/entries/Auto2_Imperative_HOL.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Constructive Cryptography in HOL</title>
       <link>/entries/Constructive_Cryptography.html</link>
       <pubDate>Mon, 17 Dec 2018 00:00:00 +0000</pubDate>
       
       <guid>/entries/Constructive_Cryptography.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Properties of Orderings and Lattices</title>
       <link>/entries/Order_Lattice_Props.html</link>
       <pubDate>Tue, 11 Dec 2018 00:00:00 +0000</pubDate>
       
       <guid>/entries/Order_Lattice_Props.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Quantales</title>
       <link>/entries/Quantales.html</link>
       <pubDate>Tue, 11 Dec 2018 00:00:00 +0000</pubDate>
       
       <guid>/entries/Quantales.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Transformer Semantics</title>
       <link>/entries/Transformer_Semantics.html</link>
       <pubDate>Tue, 11 Dec 2018 00:00:00 +0000</pubDate>
       
       <guid>/entries/Transformer_Semantics.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>A Verified Functional Implementation of Bachmair and Ganzinger&#39;s Ordered Resolution Prover</title>
       <link>/entries/Functional_Ordered_Resolution_Prover.html</link>
       <pubDate>Fri, 23 Nov 2018 00:00:00 +0000</pubDate>
       
       <guid>/entries/Functional_Ordered_Resolution_Prover.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Graph Saturation</title>
       <link>/entries/Graph_Saturation.html</link>
       <pubDate>Fri, 23 Nov 2018 00:00:00 +0000</pubDate>
       
       <guid>/entries/Graph_Saturation.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Auto2 Prover</title>
       <link>/entries/Auto2_HOL.html</link>
       <pubDate>Tue, 20 Nov 2018 00:00:00 +0000</pubDate>
       
       <guid>/entries/Auto2_HOL.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Matroids</title>
       <link>/entries/Matroids.html</link>
       <pubDate>Fri, 16 Nov 2018 00:00:00 +0000</pubDate>
       
       <guid>/entries/Matroids.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Deriving generic class instances for datatypes</title>
       <link>/entries/Generic_Deriving.html</link>
       <pubDate>Tue, 06 Nov 2018 00:00:00 +0000</pubDate>
       
       <guid>/entries/Generic_Deriving.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Formalisation and Evaluation of Alan Gewirth&#39;s Proof for the Principle of Generic Consistency in Isabelle/HOL</title>
       <link>/entries/GewirthPGCProof.html</link>
       <pubDate>Tue, 30 Oct 2018 00:00:00 +0000</pubDate>
       
       <guid>/entries/GewirthPGCProof.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Epistemic Logic: Completeness of Modal Logics</title>
       <link>/entries/Epistemic_Logic.html</link>
       <pubDate>Mon, 29 Oct 2018 00:00:00 +0000</pubDate>
       
       <guid>/entries/Epistemic_Logic.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Smooth Manifolds</title>
       <link>/entries/Smooth_Manifolds.html</link>
       <pubDate>Mon, 22 Oct 2018 00:00:00 +0000</pubDate>
       
       <guid>/entries/Smooth_Manifolds.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Formalization of the Embedding Path Order for Lambda-Free Higher-Order Terms</title>
       <link>/entries/Lambda_Free_EPO.html</link>
       <pubDate>Fri, 19 Oct 2018 00:00:00 +0000</pubDate>
       
       <guid>/entries/Lambda_Free_EPO.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Randomised Binary Search Trees</title>
       <link>/entries/Randomised_BSTs.html</link>
       <pubDate>Fri, 19 Oct 2018 00:00:00 +0000</pubDate>
       
       <guid>/entries/Randomised_BSTs.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Upper Bounding Diameters of State Spaces of Factored Transition Systems</title>
       <link>/entries/Factored_Transition_System_Bounding.html</link>
       <pubDate>Fri, 12 Oct 2018 00:00:00 +0000</pubDate>
       
       <guid>/entries/Factored_Transition_System_Bounding.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>The Transcendence of π</title>
       <link>/entries/Pi_Transcendental.html</link>
       <pubDate>Fri, 28 Sep 2018 00:00:00 +0000</pubDate>
       
       <guid>/entries/Pi_Transcendental.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Symmetric Polynomials</title>
       <link>/entries/Symmetric_Polynomials.html</link>
       <pubDate>Tue, 25 Sep 2018 00:00:00 +0000</pubDate>
       
       <guid>/entries/Symmetric_Polynomials.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Signature-Based Gröbner Basis Algorithms</title>
       <link>/entries/Signature_Groebner.html</link>
       <pubDate>Thu, 20 Sep 2018 00:00:00 +0000</pubDate>
       
       <guid>/entries/Signature_Groebner.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>The Prime Number Theorem</title>
       <link>/entries/Prime_Number_Theorem.html</link>
       <pubDate>Wed, 19 Sep 2018 00:00:00 +0000</pubDate>
       
       <guid>/entries/Prime_Number_Theorem.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Aggregation Algebras</title>
       <link>/entries/Aggregation_Algebras.html</link>
       <pubDate>Sat, 15 Sep 2018 00:00:00 +0000</pubDate>
       
       <guid>/entries/Aggregation_Algebras.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Octonions</title>
       <link>/entries/Octonions.html</link>
       <pubDate>Fri, 14 Sep 2018 00:00:00 +0000</pubDate>
       
       <guid>/entries/Octonions.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Quaternions</title>
       <link>/entries/Quaternions.html</link>
       <pubDate>Wed, 05 Sep 2018 00:00:00 +0000</pubDate>
       
       <guid>/entries/Quaternions.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>The Budan-Fourier Theorem and Counting Real Roots with Multiplicity</title>
       <link>/entries/Budan_Fourier.html</link>
       <pubDate>Sun, 02 Sep 2018 00:00:00 +0000</pubDate>
       
       <guid>/entries/Budan_Fourier.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>An Incremental Simplex Algorithm with Unsatisfiable Core Generation</title>
       <link>/entries/Simplex.html</link>
       <pubDate>Fri, 24 Aug 2018 00:00:00 +0000</pubDate>
       
       <guid>/entries/Simplex.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Minsky Machines</title>
       <link>/entries/Minsky_Machines.html</link>
       <pubDate>Tue, 14 Aug 2018 00:00:00 +0000</pubDate>
       
       <guid>/entries/Minsky_Machines.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Pricing in discrete financial models</title>
       <link>/entries/DiscretePricing.html</link>
       <pubDate>Mon, 16 Jul 2018 00:00:00 +0000</pubDate>
       
       <guid>/entries/DiscretePricing.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Von-Neumann-Morgenstern Utility Theorem</title>
       <link>/entries/Neumann_Morgenstern_Utility.html</link>
       <pubDate>Wed, 04 Jul 2018 00:00:00 +0000</pubDate>
       
       <guid>/entries/Neumann_Morgenstern_Utility.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Pell&#39;s Equation</title>
       <link>/entries/Pell.html</link>
       <pubDate>Sat, 23 Jun 2018 00:00:00 +0000</pubDate>
       
       <guid>/entries/Pell.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Projective Geometry</title>
       <link>/entries/Projective_Geometry.html</link>
       <pubDate>Thu, 14 Jun 2018 00:00:00 +0000</pubDate>
       
       <guid>/entries/Projective_Geometry.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>The Localization of a Commutative Ring</title>
       <link>/entries/Localization_Ring.html</link>
       <pubDate>Thu, 14 Jun 2018 00:00:00 +0000</pubDate>
       
       <guid>/entries/Localization_Ring.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Partial Order Reduction</title>
       <link>/entries/Partial_Order_Reduction.html</link>
       <pubDate>Tue, 05 Jun 2018 00:00:00 +0000</pubDate>
       
       <guid>/entries/Partial_Order_Reduction.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Optimal Binary Search Trees</title>
       <link>/entries/Optimal_BST.html</link>
       <pubDate>Sun, 27 May 2018 00:00:00 +0000</pubDate>
       
       <guid>/entries/Optimal_BST.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Hidden Markov Models</title>
       <link>/entries/Hidden_Markov_Models.html</link>
       <pubDate>Fri, 25 May 2018 00:00:00 +0000</pubDate>
       
       <guid>/entries/Hidden_Markov_Models.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Probabilistic Timed Automata</title>
       <link>/entries/Probabilistic_Timed_Automata.html</link>
       <pubDate>Thu, 24 May 2018 00:00:00 +0000</pubDate>
       
       <guid>/entries/Probabilistic_Timed_Automata.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Axiom Systems for Category Theory in Free Logic</title>
       <link>/entries/AxiomaticCategoryTheory.html</link>
       <pubDate>Wed, 23 May 2018 00:00:00 +0000</pubDate>
       
       <guid>/entries/AxiomaticCategoryTheory.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Irrational Rapidly Convergent Series</title>
       <link>/entries/Irrationality_J_Hancl.html</link>
       <pubDate>Wed, 23 May 2018 00:00:00 +0000</pubDate>
       
       <guid>/entries/Irrationality_J_Hancl.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Monadification, Memoization and Dynamic Programming</title>
       <link>/entries/Monad_Memo_DP.html</link>
       <pubDate>Tue, 22 May 2018 00:00:00 +0000</pubDate>
       
       <guid>/entries/Monad_Memo_DP.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>OpSets: Sequential Specifications for Replicated Datatypes</title>
       <link>/entries/OpSets.html</link>
       <pubDate>Thu, 10 May 2018 00:00:00 +0000</pubDate>
       
       <guid>/entries/OpSets.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>An Isabelle/HOL Formalization of the Modular Assembly Kit for Security Properties</title>
       <link>/entries/Modular_Assembly_Kit_Security.html</link>
       <pubDate>Mon, 07 May 2018 00:00:00 +0000</pubDate>
       
       <guid>/entries/Modular_Assembly_Kit_Security.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>WebAssembly</title>
       <link>/entries/WebAssembly.html</link>
       <pubDate>Sun, 29 Apr 2018 00:00:00 +0000</pubDate>
       
       <guid>/entries/WebAssembly.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>VerifyThis 2018 - Polished Isabelle Solutions</title>
       <link>/entries/VerifyThis2018.html</link>
       <pubDate>Fri, 27 Apr 2018 00:00:00 +0000</pubDate>
       
       <guid>/entries/VerifyThis2018.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Bounded Natural Functors with Covariance and Contravariance</title>
       <link>/entries/BNF_CC.html</link>
       <pubDate>Tue, 24 Apr 2018 00:00:00 +0000</pubDate>
       
       <guid>/entries/BNF_CC.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>The Incompatibility of Fishburn-Strategyproofness and Pareto-Efficiency</title>
       <link>/entries/Fishburn_Impossibility.html</link>
       <pubDate>Thu, 22 Mar 2018 00:00:00 +0000</pubDate>
       
       <guid>/entries/Fishburn_Impossibility.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Weight-Balanced Trees</title>
       <link>/entries/Weight_Balanced_Trees.html</link>
       <pubDate>Tue, 13 Mar 2018 00:00:00 +0000</pubDate>
       
       <guid>/entries/Weight_Balanced_Trees.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>CakeML</title>
       <link>/entries/CakeML.html</link>
       <pubDate>Mon, 12 Mar 2018 00:00:00 +0000</pubDate>
       
       <guid>/entries/CakeML.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>A Theory of Architectural Design Patterns</title>
       <link>/entries/Architectural_Design_Patterns.html</link>
       <pubDate>Thu, 01 Mar 2018 00:00:00 +0000</pubDate>
       
       <guid>/entries/Architectural_Design_Patterns.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Hoare Logics for Time Bounds</title>
       <link>/entries/Hoare_Time.html</link>
       <pubDate>Mon, 26 Feb 2018 00:00:00 +0000</pubDate>
       
       <guid>/entries/Hoare_Time.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>A verified factorization algorithm for integer polynomials with polynomial complexity</title>
       <link>/entries/LLL_Factorization.html</link>
       <pubDate>Tue, 06 Feb 2018 00:00:00 +0000</pubDate>
       
       <guid>/entries/LLL_Factorization.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>First-Order Terms</title>
       <link>/entries/First_Order_Terms.html</link>
       <pubDate>Tue, 06 Feb 2018 00:00:00 +0000</pubDate>
       
       <guid>/entries/First_Order_Terms.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>The Error Function</title>
       <link>/entries/Error_Function.html</link>
       <pubDate>Tue, 06 Feb 2018 00:00:00 +0000</pubDate>
       
       <guid>/entries/Error_Function.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Treaps</title>
       <link>/entries/Treaps.html</link>
       <pubDate>Tue, 06 Feb 2018 00:00:00 +0000</pubDate>
       
       <guid>/entries/Treaps.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>A verified LLL algorithm</title>
       <link>/entries/LLL_Basis_Reduction.html</link>
       <pubDate>Fri, 02 Feb 2018 00:00:00 +0000</pubDate>
       
       <guid>/entries/LLL_Basis_Reduction.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Formalization of Bachmair and Ganzinger&#39;s Ordered Resolution Prover</title>
       <link>/entries/Ordered_Resolution_Prover.html</link>
       <pubDate>Thu, 18 Jan 2018 00:00:00 +0000</pubDate>
       
       <guid>/entries/Ordered_Resolution_Prover.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Gromov Hyperbolicity</title>
       <link>/entries/Gromov_Hyperbolicity.html</link>
       <pubDate>Tue, 16 Jan 2018 00:00:00 +0000</pubDate>
       
       <guid>/entries/Gromov_Hyperbolicity.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>An Isabelle/HOL formalisation of Green&#39;s Theorem</title>
       <link>/entries/Green.html</link>
       <pubDate>Thu, 11 Jan 2018 00:00:00 +0000</pubDate>
       
       <guid>/entries/Green.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Taylor Models</title>
       <link>/entries/Taylor_Models.html</link>
       <pubDate>Mon, 08 Jan 2018 00:00:00 +0000</pubDate>
       
       <guid>/entries/Taylor_Models.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>The Falling Factorial of a Sum</title>
       <link>/entries/Falling_Factorial_Sum.html</link>
       <pubDate>Fri, 22 Dec 2017 00:00:00 +0000</pubDate>
       
       <guid>/entries/Falling_Factorial_Sum.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Dirichlet L-Functions and Dirichlet&#39;s Theorem</title>
       <link>/entries/Dirichlet_L.html</link>
       <pubDate>Thu, 21 Dec 2017 00:00:00 +0000</pubDate>
       
       <guid>/entries/Dirichlet_L.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>The Mason–Stothers Theorem</title>
       <link>/entries/Mason_Stothers.html</link>
       <pubDate>Thu, 21 Dec 2017 00:00:00 +0000</pubDate>
       
       <guid>/entries/Mason_Stothers.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>The Median-of-Medians Selection Algorithm</title>
       <link>/entries/Median_Of_Medians_Selection.html</link>
       <pubDate>Thu, 21 Dec 2017 00:00:00 +0000</pubDate>
       
       <guid>/entries/Median_Of_Medians_Selection.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Operations on Bounded Natural Functors</title>
       <link>/entries/BNF_Operations.html</link>
       <pubDate>Tue, 19 Dec 2017 00:00:00 +0000</pubDate>
       
       <guid>/entries/BNF_Operations.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>The string search algorithm by Knuth, Morris and Pratt</title>
       <link>/entries/Knuth_Morris_Pratt.html</link>
       <pubDate>Mon, 18 Dec 2017 00:00:00 +0000</pubDate>
       
       <guid>/entries/Knuth_Morris_Pratt.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Stochastic Matrices and the Perron-Frobenius Theorem</title>
       <link>/entries/Stochastic_Matrices.html</link>
       <pubDate>Wed, 22 Nov 2017 00:00:00 +0000</pubDate>
       
       <guid>/entries/Stochastic_Matrices.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>The IMAP CmRDT</title>
       <link>/entries/IMAP-CRDT.html</link>
       <pubDate>Thu, 09 Nov 2017 00:00:00 +0000</pubDate>
       
       <guid>/entries/IMAP-CRDT.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Hybrid Multi-Lane Spatial Logic</title>
       <link>/entries/Hybrid_Multi_Lane_Spatial_Logic.html</link>
       <pubDate>Mon, 06 Nov 2017 00:00:00 +0000</pubDate>
       
       <guid>/entries/Hybrid_Multi_Lane_Spatial_Logic.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>The Kuratowski Closure-Complement Theorem</title>
       <link>/entries/Kuratowski_Closure_Complement.html</link>
       <pubDate>Thu, 26 Oct 2017 00:00:00 +0000</pubDate>
       
       <guid>/entries/Kuratowski_Closure_Complement.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Büchi Complementation</title>
       <link>/entries/Buchi_Complementation.html</link>
       <pubDate>Thu, 19 Oct 2017 00:00:00 +0000</pubDate>
       
       <guid>/entries/Buchi_Complementation.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Transition Systems and Automata</title>
       <link>/entries/Transition_Systems_and_Automata.html</link>
       <pubDate>Thu, 19 Oct 2017 00:00:00 +0000</pubDate>
       
       <guid>/entries/Transition_Systems_and_Automata.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Count the Number of Complex Roots</title>
       <link>/entries/Count_Complex_Roots.html</link>
       <pubDate>Tue, 17 Oct 2017 00:00:00 +0000</pubDate>
       
       <guid>/entries/Count_Complex_Roots.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Evaluate Winding Numbers through Cauchy Indices</title>
       <link>/entries/Winding_Number_Eval.html</link>
       <pubDate>Tue, 17 Oct 2017 00:00:00 +0000</pubDate>
       
       <guid>/entries/Winding_Number_Eval.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Homogeneous Linear Diophantine Equations</title>
       <link>/entries/Diophantine_Eqns_Lin_Hom.html</link>
       <pubDate>Sat, 14 Oct 2017 00:00:00 +0000</pubDate>
       
       <guid>/entries/Diophantine_Eqns_Lin_Hom.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Dirichlet Series</title>
       <link>/entries/Dirichlet_Series.html</link>
       <pubDate>Thu, 12 Oct 2017 00:00:00 +0000</pubDate>
       
       <guid>/entries/Dirichlet_Series.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Linear Recurrences</title>
       <link>/entries/Linear_Recurrences.html</link>
       <pubDate>Thu, 12 Oct 2017 00:00:00 +0000</pubDate>
       
       <guid>/entries/Linear_Recurrences.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>The Hurwitz and Riemann ζ Functions</title>
       <link>/entries/Zeta_Function.html</link>
       <pubDate>Thu, 12 Oct 2017 00:00:00 +0000</pubDate>
       
       <guid>/entries/Zeta_Function.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Computer-assisted Reconstruction and Assessment of E. J. Lowe&#39;s Modal Ontological Argument</title>
       <link>/entries/Lowe_Ontological_Argument.html</link>
       <pubDate>Thu, 21 Sep 2017 00:00:00 +0000</pubDate>
       
       <guid>/entries/Lowe_Ontological_Argument.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Representation and Partial Automation of the Principia Logico-Metaphysica in Isabelle/HOL</title>
       <link>/entries/PLM.html</link>
       <pubDate>Sun, 17 Sep 2017 00:00:00 +0000</pubDate>
       
       <guid>/entries/PLM.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Anselm&#39;s God in Isabelle/HOL</title>
       <link>/entries/AnselmGod.html</link>
       <pubDate>Wed, 06 Sep 2017 00:00:00 +0000</pubDate>
       
       <guid>/entries/AnselmGod.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Microeconomics and the First Welfare Theorem</title>
       <link>/entries/First_Welfare_Theorem.html</link>
       <pubDate>Fri, 01 Sep 2017 00:00:00 +0000</pubDate>
       
       <guid>/entries/First_Welfare_Theorem.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Orbit-Stabiliser Theorem with Application to Rotational Symmetries</title>
       <link>/entries/Orbit_Stabiliser.html</link>
       <pubDate>Sun, 20 Aug 2017 00:00:00 +0000</pubDate>
       
       <guid>/entries/Orbit_Stabiliser.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Root-Balanced Tree</title>
       <link>/entries/Root_Balanced_Tree.html</link>
       <pubDate>Sun, 20 Aug 2017 00:00:00 +0000</pubDate>
       
       <guid>/entries/Root_Balanced_Tree.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>The LambdaMu-calculus</title>
       <link>/entries/LambdaMu.html</link>
       <pubDate>Wed, 16 Aug 2017 00:00:00 +0000</pubDate>
       
       <guid>/entries/LambdaMu.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Stewart&#39;s Theorem and Apollonius&#39; Theorem</title>
       <link>/entries/Stewart_Apollonius.html</link>
       <pubDate>Mon, 31 Jul 2017 00:00:00 +0000</pubDate>
       
       <guid>/entries/Stewart_Apollonius.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Dynamic Architectures</title>
       <link>/entries/DynamicArchitectures.html</link>
       <pubDate>Fri, 28 Jul 2017 00:00:00 +0000</pubDate>
       
       <guid>/entries/DynamicArchitectures.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Declarative Semantics for Functional Languages</title>
       <link>/entries/Decl_Sem_Fun_PL.html</link>
       <pubDate>Fri, 21 Jul 2017 00:00:00 +0000</pubDate>
       
       <guid>/entries/Decl_Sem_Fun_PL.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>HOLCF-Prelude</title>
       <link>/entries/HOLCF-Prelude.html</link>
       <pubDate>Sat, 15 Jul 2017 00:00:00 +0000</pubDate>
       
       <guid>/entries/HOLCF-Prelude.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Minkowski&#39;s Theorem</title>
       <link>/entries/Minkowskis_Theorem.html</link>
       <pubDate>Thu, 13 Jul 2017 00:00:00 +0000</pubDate>
       
       <guid>/entries/Minkowskis_Theorem.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Verified Metatheory and Type Inference for a Name-Carrying Simply-Typed Lambda Calculus</title>
       <link>/entries/Name_Carrying_Type_Inference.html</link>
       <pubDate>Sun, 09 Jul 2017 00:00:00 +0000</pubDate>
       
       <guid>/entries/Name_Carrying_Type_Inference.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>A framework for establishing Strong Eventual Consistency for Conflict-free Replicated Datatypes</title>
       <link>/entries/CRDT.html</link>
       <pubDate>Fri, 07 Jul 2017 00:00:00 +0000</pubDate>
       
       <guid>/entries/CRDT.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Stone-Kleene Relation Algebras</title>
       <link>/entries/Stone_Kleene_Relation_Algebras.html</link>
       <pubDate>Thu, 06 Jul 2017 00:00:00 +0000</pubDate>
       
       <guid>/entries/Stone_Kleene_Relation_Algebras.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Propositional Proof Systems</title>
       <link>/entries/Propositional_Proof_Systems.html</link>
       <pubDate>Wed, 21 Jun 2017 00:00:00 +0000</pubDate>
       
       <guid>/entries/Propositional_Proof_Systems.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Partial Semigroups and Convolution Algebras</title>
       <link>/entries/PSemigroupsConvolution.html</link>
       <pubDate>Tue, 13 Jun 2017 00:00:00 +0000</pubDate>
       
       <guid>/entries/PSemigroupsConvolution.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Buffon&#39;s Needle Problem</title>
       <link>/entries/Buffons_Needle.html</link>
       <pubDate>Tue, 06 Jun 2017 00:00:00 +0000</pubDate>
       
       <guid>/entries/Buffons_Needle.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Flow Networks and the Min-Cut-Max-Flow Theorem</title>
       <link>/entries/Flow_Networks.html</link>
       <pubDate>Thu, 01 Jun 2017 00:00:00 +0000</pubDate>
       
       <guid>/entries/Flow_Networks.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Formalizing Push-Relabel Algorithms</title>
       <link>/entries/Prpu_Maxflow.html</link>
       <pubDate>Thu, 01 Jun 2017 00:00:00 +0000</pubDate>
       
       <guid>/entries/Prpu_Maxflow.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Optics</title>
       <link>/entries/Optics.html</link>
       <pubDate>Thu, 25 May 2017 00:00:00 +0000</pubDate>
       
       <guid>/entries/Optics.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Developing Security Protocols by Refinement</title>
       <link>/entries/Security_Protocol_Refinement.html</link>
       <pubDate>Wed, 24 May 2017 00:00:00 +0000</pubDate>
       
       <guid>/entries/Security_Protocol_Refinement.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Dictionary Construction</title>
       <link>/entries/Dict_Construction.html</link>
       <pubDate>Wed, 24 May 2017 00:00:00 +0000</pubDate>
       
       <guid>/entries/Dict_Construction.html</guid>
       <description></description>
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     <item>
       <title>The Floyd-Warshall Algorithm for Shortest Paths</title>
       <link>/entries/Floyd_Warshall.html</link>
       <pubDate>Mon, 08 May 2017 00:00:00 +0000</pubDate>
       
       <guid>/entries/Floyd_Warshall.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>CryptHOL</title>
       <link>/entries/CryptHOL.html</link>
       <pubDate>Fri, 05 May 2017 00:00:00 +0000</pubDate>
       
       <guid>/entries/CryptHOL.html</guid>
       <description></description>
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     <item>
       <title>Effect polymorphism in higher-order logic</title>
       <link>/entries/Monomorphic_Monad.html</link>
       <pubDate>Fri, 05 May 2017 00:00:00 +0000</pubDate>
       
       <guid>/entries/Monomorphic_Monad.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Game-based cryptography in HOL</title>
       <link>/entries/Game_Based_Crypto.html</link>
       <pubDate>Fri, 05 May 2017 00:00:00 +0000</pubDate>
       
       <guid>/entries/Game_Based_Crypto.html</guid>
       <description></description>
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     <item>
       <title>Monad normalisation</title>
       <link>/entries/Monad_Normalisation.html</link>
       <pubDate>Fri, 05 May 2017 00:00:00 +0000</pubDate>
       
       <guid>/entries/Monad_Normalisation.html</guid>
       <description></description>
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     <item>
       <title>Probabilistic while loop</title>
       <link>/entries/Probabilistic_While.html</link>
       <pubDate>Fri, 05 May 2017 00:00:00 +0000</pubDate>
       
       <guid>/entries/Probabilistic_While.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Monoidal Categories</title>
       <link>/entries/MonoidalCategory.html</link>
       <pubDate>Thu, 04 May 2017 00:00:00 +0000</pubDate>
       
       <guid>/entries/MonoidalCategory.html</guid>
       <description></description>
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     <item>
       <title>Types, Tableaus and Gödel’s God in Isabelle/HOL</title>
       <link>/entries/Types_Tableaus_and_Goedels_God.html</link>
       <pubDate>Mon, 01 May 2017 00:00:00 +0000</pubDate>
       
       <guid>/entries/Types_Tableaus_and_Goedels_God.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Local Lexing</title>
       <link>/entries/LocalLexing.html</link>
       <pubDate>Fri, 28 Apr 2017 00:00:00 +0000</pubDate>
       
       <guid>/entries/LocalLexing.html</guid>
       <description></description>
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     <item>
       <title>Constructor Functions</title>
       <link>/entries/Constructor_Funs.html</link>
       <pubDate>Wed, 19 Apr 2017 00:00:00 +0000</pubDate>
       
       <guid>/entries/Constructor_Funs.html</guid>
       <description></description>
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     <item>
       <title>Lazifying case constants</title>
       <link>/entries/Lazy_Case.html</link>
       <pubDate>Tue, 18 Apr 2017 00:00:00 +0000</pubDate>
       
       <guid>/entries/Lazy_Case.html</guid>
       <description></description>
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     <item>
       <title>Subresultants</title>
       <link>/entries/Subresultants.html</link>
       <pubDate>Thu, 06 Apr 2017 00:00:00 +0000</pubDate>
       
       <guid>/entries/Subresultants.html</guid>
       <description></description>
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     <item>
       <title>Expected Shape of Random Binary Search Trees</title>
       <link>/entries/Random_BSTs.html</link>
       <pubDate>Tue, 04 Apr 2017 00:00:00 +0000</pubDate>
       
       <guid>/entries/Random_BSTs.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Lower bound on comparison-based sorting algorithms</title>
       <link>/entries/Comparison_Sort_Lower_Bound.html</link>
       <pubDate>Wed, 15 Mar 2017 00:00:00 +0000</pubDate>
       
       <guid>/entries/Comparison_Sort_Lower_Bound.html</guid>
       <description></description>
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     <item>
       <title>The number of comparisons in QuickSort</title>
       <link>/entries/Quick_Sort_Cost.html</link>
       <pubDate>Wed, 15 Mar 2017 00:00:00 +0000</pubDate>
       
       <guid>/entries/Quick_Sort_Cost.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>The Euler–MacLaurin Formula</title>
       <link>/entries/Euler_MacLaurin.html</link>
       <pubDate>Fri, 10 Mar 2017 00:00:00 +0000</pubDate>
       
       <guid>/entries/Euler_MacLaurin.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>The Group Law for Elliptic Curves</title>
       <link>/entries/Elliptic_Curves_Group_Law.html</link>
       <pubDate>Tue, 28 Feb 2017 00:00:00 +0000</pubDate>
       
       <guid>/entries/Elliptic_Curves_Group_Law.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Menger&#39;s Theorem</title>
       <link>/entries/Menger.html</link>
       <pubDate>Sun, 26 Feb 2017 00:00:00 +0000</pubDate>
       
       <guid>/entries/Menger.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Differential Dynamic Logic</title>
       <link>/entries/Differential_Dynamic_Logic.html</link>
       <pubDate>Mon, 13 Feb 2017 00:00:00 +0000</pubDate>
       
       <guid>/entries/Differential_Dynamic_Logic.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Abstract Soundness</title>
       <link>/entries/Abstract_Soundness.html</link>
       <pubDate>Fri, 10 Feb 2017 00:00:00 +0000</pubDate>
       
       <guid>/entries/Abstract_Soundness.html</guid>
       <description></description>
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     <item>
       <title>Stone Relation Algebras</title>
       <link>/entries/Stone_Relation_Algebras.html</link>
       <pubDate>Tue, 07 Feb 2017 00:00:00 +0000</pubDate>
       
       <guid>/entries/Stone_Relation_Algebras.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Refining Authenticated Key Agreement with Strong Adversaries</title>
       <link>/entries/Key_Agreement_Strong_Adversaries.html</link>
       <pubDate>Tue, 31 Jan 2017 00:00:00 +0000</pubDate>
       
       <guid>/entries/Key_Agreement_Strong_Adversaries.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Bernoulli Numbers</title>
       <link>/entries/Bernoulli.html</link>
       <pubDate>Tue, 24 Jan 2017 00:00:00 +0000</pubDate>
       
       <guid>/entries/Bernoulli.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Bertrand&#39;s postulate</title>
       <link>/entries/Bertrands_Postulate.html</link>
       <pubDate>Tue, 17 Jan 2017 00:00:00 +0000</pubDate>
       
       <guid>/entries/Bertrands_Postulate.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Minimal Static Single Assignment Form</title>
       <link>/entries/Minimal_SSA.html</link>
       <pubDate>Tue, 17 Jan 2017 00:00:00 +0000</pubDate>
       
       <guid>/entries/Minimal_SSA.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>The Transcendence of e</title>
       <link>/entries/E_Transcendental.html</link>
       <pubDate>Thu, 12 Jan 2017 00:00:00 +0000</pubDate>
       
       <guid>/entries/E_Transcendental.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Formal Network Models and Their Application to Firewall Policies</title>
       <link>/entries/UPF_Firewall.html</link>
       <pubDate>Sun, 08 Jan 2017 00:00:00 +0000</pubDate>
       
       <guid>/entries/UPF_Firewall.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Verification of a Diffie-Hellman Password-based Authentication Protocol by Extending the Inductive Method</title>
       <link>/entries/Password_Authentication_Protocol.html</link>
       <pubDate>Tue, 03 Jan 2017 00:00:00 +0000</pubDate>
       
       <guid>/entries/Password_Authentication_Protocol.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>First-Order Logic According to Harrison</title>
       <link>/entries/FOL_Harrison.html</link>
       <pubDate>Sun, 01 Jan 2017 00:00:00 +0000</pubDate>
       
       <guid>/entries/FOL_Harrison.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Concurrent Refinement Algebra and Rely Quotients</title>
       <link>/entries/Concurrent_Ref_Alg.html</link>
       <pubDate>Fri, 30 Dec 2016 00:00:00 +0000</pubDate>
       
       <guid>/entries/Concurrent_Ref_Alg.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>The Twelvefold Way</title>
       <link>/entries/Twelvefold_Way.html</link>
       <pubDate>Thu, 29 Dec 2016 00:00:00 +0000</pubDate>
       
       <guid>/entries/Twelvefold_Way.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Proof Strategy Language</title>
       <link>/entries/Proof_Strategy_Language.html</link>
       <pubDate>Tue, 20 Dec 2016 00:00:00 +0000</pubDate>
       
       <guid>/entries/Proof_Strategy_Language.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Paraconsistency</title>
       <link>/entries/Paraconsistency.html</link>
       <pubDate>Wed, 07 Dec 2016 00:00:00 +0000</pubDate>
       
       <guid>/entries/Paraconsistency.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>COMPLX: A Verification Framework for Concurrent Imperative Programs</title>
       <link>/entries/Complx.html</link>
       <pubDate>Tue, 29 Nov 2016 00:00:00 +0000</pubDate>
       
       <guid>/entries/Complx.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Abstract Interpretation of Annotated Commands</title>
       <link>/entries/Abs_Int_ITP2012.html</link>
       <pubDate>Wed, 23 Nov 2016 00:00:00 +0000</pubDate>
       
       <guid>/entries/Abs_Int_ITP2012.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Separata: Isabelle tactics for Separation Algebra</title>
       <link>/entries/Separata.html</link>
       <pubDate>Wed, 16 Nov 2016 00:00:00 +0000</pubDate>
       
       <guid>/entries/Separata.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Formalization of Knuth–Bendix Orders for Lambda-Free Higher-Order Terms</title>
       <link>/entries/Lambda_Free_KBOs.html</link>
       <pubDate>Sat, 12 Nov 2016 00:00:00 +0000</pubDate>
       
       <guid>/entries/Lambda_Free_KBOs.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Formalization of Nested Multisets, Hereditary Multisets, and Syntactic Ordinals</title>
       <link>/entries/Nested_Multisets_Ordinals.html</link>
       <pubDate>Sat, 12 Nov 2016 00:00:00 +0000</pubDate>
       
       <guid>/entries/Nested_Multisets_Ordinals.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Expressiveness of Deep Learning</title>
       <link>/entries/Deep_Learning.html</link>
       <pubDate>Thu, 10 Nov 2016 00:00:00 +0000</pubDate>
       
       <guid>/entries/Deep_Learning.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Modal Logics for Nominal Transition Systems</title>
       <link>/entries/Modal_Logics_for_NTS.html</link>
       <pubDate>Tue, 25 Oct 2016 00:00:00 +0000</pubDate>
       
       <guid>/entries/Modal_Logics_for_NTS.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Stable Matching</title>
       <link>/entries/Stable_Matching.html</link>
       <pubDate>Mon, 24 Oct 2016 00:00:00 +0000</pubDate>
       
       <guid>/entries/Stable_Matching.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>LOFT — Verified Migration of Linux Firewalls to SDN</title>
       <link>/entries/LOFT.html</link>
       <pubDate>Fri, 21 Oct 2016 00:00:00 +0000</pubDate>
       
       <guid>/entries/LOFT.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>A formal model for the SPARCv8 ISA and a proof of non-interference for the LEON3 processor</title>
       <link>/entries/SPARCv8.html</link>
       <pubDate>Wed, 19 Oct 2016 00:00:00 +0000</pubDate>
       
       <guid>/entries/SPARCv8.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Source Coding Theorem</title>
       <link>/entries/Source_Coding_Theorem.html</link>
       <pubDate>Wed, 19 Oct 2016 00:00:00 +0000</pubDate>
       
       <guid>/entries/Source_Coding_Theorem.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>The Factorization Algorithm of Berlekamp and Zassenhaus</title>
       <link>/entries/Berlekamp_Zassenhaus.html</link>
       <pubDate>Fri, 14 Oct 2016 00:00:00 +0000</pubDate>
       
       <guid>/entries/Berlekamp_Zassenhaus.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Intersecting Chords Theorem</title>
       <link>/entries/Chord_Segments.html</link>
       <pubDate>Tue, 11 Oct 2016 00:00:00 +0000</pubDate>
       
       <guid>/entries/Chord_Segments.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Lp spaces</title>
       <link>/entries/Lp.html</link>
       <pubDate>Wed, 05 Oct 2016 00:00:00 +0000</pubDate>
       
       <guid>/entries/Lp.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Fisher–Yates shuffle</title>
       <link>/entries/Fisher_Yates.html</link>
       <pubDate>Fri, 30 Sep 2016 00:00:00 +0000</pubDate>
       
       <guid>/entries/Fisher_Yates.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Allen&#39;s Interval Calculus</title>
       <link>/entries/Allen_Calculus.html</link>
       <pubDate>Thu, 29 Sep 2016 00:00:00 +0000</pubDate>
       
       <guid>/entries/Allen_Calculus.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Formalization of Recursive Path Orders for Lambda-Free Higher-Order Terms</title>
       <link>/entries/Lambda_Free_RPOs.html</link>
       <pubDate>Fri, 23 Sep 2016 00:00:00 +0000</pubDate>
       
       <guid>/entries/Lambda_Free_RPOs.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Iptables Semantics</title>
       <link>/entries/Iptables_Semantics.html</link>
       <pubDate>Fri, 09 Sep 2016 00:00:00 +0000</pubDate>
       
       <guid>/entries/Iptables_Semantics.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>A Variant of the Superposition Calculus</title>
       <link>/entries/SuperCalc.html</link>
       <pubDate>Tue, 06 Sep 2016 00:00:00 +0000</pubDate>
       
       <guid>/entries/SuperCalc.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Stone Algebras</title>
       <link>/entries/Stone_Algebras.html</link>
       <pubDate>Tue, 06 Sep 2016 00:00:00 +0000</pubDate>
       
       <guid>/entries/Stone_Algebras.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Stirling&#39;s formula</title>
       <link>/entries/Stirling_Formula.html</link>
       <pubDate>Thu, 01 Sep 2016 00:00:00 +0000</pubDate>
       
       <guid>/entries/Stirling_Formula.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Routing</title>
       <link>/entries/Routing.html</link>
       <pubDate>Wed, 31 Aug 2016 00:00:00 +0000</pubDate>
       
       <guid>/entries/Routing.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Simple Firewall</title>
       <link>/entries/Simple_Firewall.html</link>
       <pubDate>Wed, 24 Aug 2016 00:00:00 +0000</pubDate>
       
       <guid>/entries/Simple_Firewall.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Infeasible Paths Elimination by Symbolic Execution Techniques: Proof of Correctness and Preservation of Paths</title>
       <link>/entries/InfPathElimination.html</link>
       <pubDate>Thu, 18 Aug 2016 00:00:00 +0000</pubDate>
       
       <guid>/entries/InfPathElimination.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Formalizing the Edmonds-Karp Algorithm</title>
       <link>/entries/EdmondsKarp_Maxflow.html</link>
       <pubDate>Fri, 12 Aug 2016 00:00:00 +0000</pubDate>
       
       <guid>/entries/EdmondsKarp_Maxflow.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>The Imperative Refinement Framework</title>
       <link>/entries/Refine_Imperative_HOL.html</link>
       <pubDate>Mon, 08 Aug 2016 00:00:00 +0000</pubDate>
       
       <guid>/entries/Refine_Imperative_HOL.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Ptolemy&#39;s Theorem</title>
       <link>/entries/Ptolemys_Theorem.html</link>
       <pubDate>Sun, 07 Aug 2016 00:00:00 +0000</pubDate>
       
       <guid>/entries/Ptolemys_Theorem.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Surprise Paradox</title>
       <link>/entries/Surprise_Paradox.html</link>
       <pubDate>Sun, 17 Jul 2016 00:00:00 +0000</pubDate>
       
       <guid>/entries/Surprise_Paradox.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Pairing Heap</title>
       <link>/entries/Pairing_Heap.html</link>
       <pubDate>Thu, 14 Jul 2016 00:00:00 +0000</pubDate>
       
       <guid>/entries/Pairing_Heap.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>A Framework for Verifying Depth-First Search Algorithms</title>
       <link>/entries/DFS_Framework.html</link>
       <pubDate>Tue, 05 Jul 2016 00:00:00 +0000</pubDate>
       
       <guid>/entries/DFS_Framework.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Chamber Complexes, Coxeter Systems, and Buildings</title>
       <link>/entries/Buildings.html</link>
       <pubDate>Fri, 01 Jul 2016 00:00:00 +0000</pubDate>
       
       <guid>/entries/Buildings.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>The Resolution Calculus for First-Order Logic</title>
       <link>/entries/Resolution_FOL.html</link>
       <pubDate>Thu, 30 Jun 2016 00:00:00 +0000</pubDate>
       
       <guid>/entries/Resolution_FOL.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>The Z Property</title>
       <link>/entries/Rewriting_Z.html</link>
       <pubDate>Thu, 30 Jun 2016 00:00:00 +0000</pubDate>
       
       <guid>/entries/Rewriting_Z.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Compositional Security-Preserving Refinement for Concurrent Imperative Programs</title>
       <link>/entries/Dependent_SIFUM_Refinement.html</link>
       <pubDate>Tue, 28 Jun 2016 00:00:00 +0000</pubDate>
       
       <guid>/entries/Dependent_SIFUM_Refinement.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>IP Addresses</title>
       <link>/entries/IP_Addresses.html</link>
       <pubDate>Tue, 28 Jun 2016 00:00:00 +0000</pubDate>
       
       <guid>/entries/IP_Addresses.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Cardinality of Multisets</title>
       <link>/entries/Card_Multisets.html</link>
       <pubDate>Sun, 26 Jun 2016 00:00:00 +0000</pubDate>
       
       <guid>/entries/Card_Multisets.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Category Theory with Adjunctions and Limits</title>
       <link>/entries/Category3.html</link>
       <pubDate>Sun, 26 Jun 2016 00:00:00 +0000</pubDate>
       
       <guid>/entries/Category3.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>A Dependent Security Type System for Concurrent Imperative Programs</title>
       <link>/entries/Dependent_SIFUM_Type_Systems.html</link>
       <pubDate>Sat, 25 Jun 2016 00:00:00 +0000</pubDate>
       
       <guid>/entries/Dependent_SIFUM_Type_Systems.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Catalan Numbers</title>
       <link>/entries/Catalan_Numbers.html</link>
       <pubDate>Tue, 21 Jun 2016 00:00:00 +0000</pubDate>
       
       <guid>/entries/Catalan_Numbers.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Program Construction and Verification Components Based on Kleene Algebra</title>
       <link>/entries/Algebraic_VCs.html</link>
       <pubDate>Sat, 18 Jun 2016 00:00:00 +0000</pubDate>
       
       <guid>/entries/Algebraic_VCs.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Conservation of CSP Noninterference Security under Concurrent Composition</title>
       <link>/entries/Noninterference_Concurrent_Composition.html</link>
       <pubDate>Mon, 13 Jun 2016 00:00:00 +0000</pubDate>
       
       <guid>/entries/Noninterference_Concurrent_Composition.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Finite Machine Word Library</title>
       <link>/entries/Word_Lib.html</link>
       <pubDate>Thu, 09 Jun 2016 00:00:00 +0000</pubDate>
       
       <guid>/entries/Word_Lib.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Tree Decomposition</title>
       <link>/entries/Tree_Decomposition.html</link>
       <pubDate>Tue, 31 May 2016 00:00:00 +0000</pubDate>
       
       <guid>/entries/Tree_Decomposition.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Cardinality of Equivalence Relations</title>
       <link>/entries/Card_Equiv_Relations.html</link>
       <pubDate>Tue, 24 May 2016 00:00:00 +0000</pubDate>
       
       <guid>/entries/Card_Equiv_Relations.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>POSIX Lexing with Derivatives of Regular Expressions</title>
       <link>/entries/Posix-Lexing.html</link>
       <pubDate>Tue, 24 May 2016 00:00:00 +0000</pubDate>
       
       <guid>/entries/Posix-Lexing.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Perron-Frobenius Theorem for Spectral Radius Analysis</title>
       <link>/entries/Perron_Frobenius.html</link>
       <pubDate>Fri, 20 May 2016 00:00:00 +0000</pubDate>
       
       <guid>/entries/Perron_Frobenius.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>The meta theory of the Incredible Proof Machine</title>
       <link>/entries/Incredible_Proof_Machine.html</link>
       <pubDate>Fri, 20 May 2016 00:00:00 +0000</pubDate>
       
       <guid>/entries/Incredible_Proof_Machine.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>A Constructive Proof for FLP</title>
       <link>/entries/FLP.html</link>
       <pubDate>Wed, 18 May 2016 00:00:00 +0000</pubDate>
       
       <guid>/entries/FLP.html</guid>
       <description></description>
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     <item>
       <title>A Formal Proof of the Max-Flow Min-Cut Theorem for Countable Networks</title>
       <link>/entries/MFMC_Countable.html</link>
       <pubDate>Mon, 09 May 2016 00:00:00 +0000</pubDate>
       
       <guid>/entries/MFMC_Countable.html</guid>
       <description></description>
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     <item>
       <title>Randomised Social Choice Theory</title>
       <link>/entries/Randomised_Social_Choice.html</link>
       <pubDate>Thu, 05 May 2016 00:00:00 +0000</pubDate>
       
       <guid>/entries/Randomised_Social_Choice.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Spivey&#39;s Generalized Recurrence for Bell Numbers</title>
       <link>/entries/Bell_Numbers_Spivey.html</link>
       <pubDate>Wed, 04 May 2016 00:00:00 +0000</pubDate>
       
       <guid>/entries/Bell_Numbers_Spivey.html</guid>
       <description></description>
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     <item>
       <title>The Incompatibility of SD-Efficiency and SD-Strategy-Proofness</title>
       <link>/entries/SDS_Impossibility.html</link>
       <pubDate>Wed, 04 May 2016 00:00:00 +0000</pubDate>
       
       <guid>/entries/SDS_Impossibility.html</guid>
       <description></description>
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     <item>
       <title>Gröbner Bases Theory</title>
       <link>/entries/Groebner_Bases.html</link>
       <pubDate>Mon, 02 May 2016 00:00:00 +0000</pubDate>
       
       <guid>/entries/Groebner_Bases.html</guid>
       <description></description>
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     <item>
       <title>No Faster-Than-Light Observers</title>
       <link>/entries/No_FTL_observers.html</link>
       <pubDate>Thu, 28 Apr 2016 00:00:00 +0000</pubDate>
       
       <guid>/entries/No_FTL_observers.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>A formalisation of the Cocke-Younger-Kasami algorithm</title>
       <link>/entries/CYK.html</link>
       <pubDate>Wed, 27 Apr 2016 00:00:00 +0000</pubDate>
       
       <guid>/entries/CYK.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Algorithms for Reduced Ordered Binary Decision Diagrams</title>
       <link>/entries/ROBDD.html</link>
       <pubDate>Wed, 27 Apr 2016 00:00:00 +0000</pubDate>
       
       <guid>/entries/ROBDD.html</guid>
       <description></description>
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     <item>
       <title>Conservation of CSP Noninterference Security under Sequential Composition</title>
       <link>/entries/Noninterference_Sequential_Composition.html</link>
       <pubDate>Tue, 26 Apr 2016 00:00:00 +0000</pubDate>
       
       <guid>/entries/Noninterference_Sequential_Composition.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Kleene Algebras with Domain</title>
       <link>/entries/KAD.html</link>
       <pubDate>Tue, 12 Apr 2016 00:00:00 +0000</pubDate>
       
       <guid>/entries/KAD.html</guid>
       <description></description>
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     <item>
       <title>Propositional Resolution and Prime Implicates Generation</title>
       <link>/entries/PropResPI.html</link>
       <pubDate>Fri, 11 Mar 2016 00:00:00 +0000</pubDate>
       
       <guid>/entries/PropResPI.html</guid>
       <description></description>
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     <item>
       <title>The Cartan Fixed Point Theorems</title>
       <link>/entries/Cartan_FP.html</link>
       <pubDate>Tue, 08 Mar 2016 00:00:00 +0000</pubDate>
       
       <guid>/entries/Cartan_FP.html</guid>
       <description></description>
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     <item>
       <title>Timed Automata</title>
       <link>/entries/Timed_Automata.html</link>
       <pubDate>Tue, 08 Mar 2016 00:00:00 +0000</pubDate>
       
       <guid>/entries/Timed_Automata.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Linear Temporal Logic</title>
       <link>/entries/LTL.html</link>
       <pubDate>Tue, 01 Mar 2016 00:00:00 +0000</pubDate>
       
       <guid>/entries/LTL.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Analysis of List Update Algorithms</title>
       <link>/entries/List_Update.html</link>
       <pubDate>Wed, 17 Feb 2016 00:00:00 +0000</pubDate>
       
       <guid>/entries/List_Update.html</guid>
       <description></description>
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     <item>
       <title>Verified Construction of Static Single Assignment Form</title>
       <link>/entries/Formal_SSA.html</link>
       <pubDate>Fri, 05 Feb 2016 00:00:00 +0000</pubDate>
       
       <guid>/entries/Formal_SSA.html</guid>
       <description></description>
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     <item>
       <title>Polynomial Factorization</title>
       <link>/entries/Polynomial_Factorization.html</link>
       <pubDate>Fri, 29 Jan 2016 00:00:00 +0000</pubDate>
       
       <guid>/entries/Polynomial_Factorization.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Polynomial Interpolation</title>
       <link>/entries/Polynomial_Interpolation.html</link>
       <pubDate>Fri, 29 Jan 2016 00:00:00 +0000</pubDate>
       
       <guid>/entries/Polynomial_Interpolation.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Knot Theory</title>
       <link>/entries/Knot_Theory.html</link>
       <pubDate>Wed, 20 Jan 2016 00:00:00 +0000</pubDate>
       
       <guid>/entries/Knot_Theory.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Tensor Product of Matrices</title>
       <link>/entries/Matrix_Tensor.html</link>
       <pubDate>Mon, 18 Jan 2016 00:00:00 +0000</pubDate>
       
       <guid>/entries/Matrix_Tensor.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Cardinality of Number Partitions</title>
       <link>/entries/Card_Number_Partitions.html</link>
       <pubDate>Thu, 14 Jan 2016 00:00:00 +0000</pubDate>
       
       <guid>/entries/Card_Number_Partitions.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Basic Geometric Properties of Triangles</title>
       <link>/entries/Triangle.html</link>
       <pubDate>Mon, 28 Dec 2015 00:00:00 +0000</pubDate>
       
       <guid>/entries/Triangle.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Descartes&#39; Rule of Signs</title>
       <link>/entries/Descartes_Sign_Rule.html</link>
       <pubDate>Mon, 28 Dec 2015 00:00:00 +0000</pubDate>
       
       <guid>/entries/Descartes_Sign_Rule.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Liouville numbers</title>
       <link>/entries/Liouville_Numbers.html</link>
       <pubDate>Mon, 28 Dec 2015 00:00:00 +0000</pubDate>
       
       <guid>/entries/Liouville_Numbers.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>The Divergence of the Prime Harmonic Series</title>
       <link>/entries/Prime_Harmonic_Series.html</link>
       <pubDate>Mon, 28 Dec 2015 00:00:00 +0000</pubDate>
       
       <guid>/entries/Prime_Harmonic_Series.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Algebraic Numbers in Isabelle/HOL</title>
       <link>/entries/Algebraic_Numbers.html</link>
       <pubDate>Tue, 22 Dec 2015 00:00:00 +0000</pubDate>
       
       <guid>/entries/Algebraic_Numbers.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Applicative Lifting</title>
       <link>/entries/Applicative_Lifting.html</link>
       <pubDate>Tue, 22 Dec 2015 00:00:00 +0000</pubDate>
       
       <guid>/entries/Applicative_Lifting.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>The Stern-Brocot Tree</title>
       <link>/entries/Stern_Brocot.html</link>
       <pubDate>Tue, 22 Dec 2015 00:00:00 +0000</pubDate>
       
       <guid>/entries/Stern_Brocot.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Cardinality of Set Partitions</title>
       <link>/entries/Card_Partitions.html</link>
       <pubDate>Sat, 12 Dec 2015 00:00:00 +0000</pubDate>
       
       <guid>/entries/Card_Partitions.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Latin Square</title>
       <link>/entries/Latin_Square.html</link>
       <pubDate>Wed, 02 Dec 2015 00:00:00 +0000</pubDate>
       
       <guid>/entries/Latin_Square.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Ergodic Theory</title>
       <link>/entries/Ergodic_Theory.html</link>
       <pubDate>Tue, 01 Dec 2015 00:00:00 +0000</pubDate>
       
       <guid>/entries/Ergodic_Theory.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Euler&#39;s Partition Theorem</title>
       <link>/entries/Euler_Partition.html</link>
       <pubDate>Thu, 19 Nov 2015 00:00:00 +0000</pubDate>
       
       <guid>/entries/Euler_Partition.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>The Tortoise and Hare Algorithm</title>
       <link>/entries/TortoiseHare.html</link>
       <pubDate>Wed, 18 Nov 2015 00:00:00 +0000</pubDate>
       
       <guid>/entries/TortoiseHare.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Planarity Certificates</title>
       <link>/entries/Planarity_Certificates.html</link>
       <pubDate>Wed, 11 Nov 2015 00:00:00 +0000</pubDate>
       
       <guid>/entries/Planarity_Certificates.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Positional Determinacy of Parity Games</title>
       <link>/entries/Parity_Game.html</link>
       <pubDate>Mon, 02 Nov 2015 00:00:00 +0000</pubDate>
       
       <guid>/entries/Parity_Game.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>A Meta-Model for the Isabelle API</title>
       <link>/entries/Isabelle_Meta_Model.html</link>
       <pubDate>Wed, 16 Sep 2015 00:00:00 +0000</pubDate>
       
       <guid>/entries/Isabelle_Meta_Model.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Converting Linear Temporal Logic to Deterministic (Generalized) Rabin Automata</title>
       <link>/entries/LTL_to_DRA.html</link>
       <pubDate>Fri, 04 Sep 2015 00:00:00 +0000</pubDate>
       
       <guid>/entries/LTL_to_DRA.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Matrices, Jordan Normal Forms, and Spectral Radius Theory</title>
       <link>/entries/Jordan_Normal_Form.html</link>
       <pubDate>Fri, 21 Aug 2015 00:00:00 +0000</pubDate>
       
       <guid>/entries/Jordan_Normal_Form.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Decreasing Diagrams II</title>
       <link>/entries/Decreasing-Diagrams-II.html</link>
       <pubDate>Thu, 20 Aug 2015 00:00:00 +0000</pubDate>
       
       <guid>/entries/Decreasing-Diagrams-II.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>The Inductive Unwinding Theorem for CSP Noninterference Security</title>
       <link>/entries/Noninterference_Inductive_Unwinding.html</link>
       <pubDate>Tue, 18 Aug 2015 00:00:00 +0000</pubDate>
       
       <guid>/entries/Noninterference_Inductive_Unwinding.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Representations of Finite Groups</title>
       <link>/entries/Rep_Fin_Groups.html</link>
       <pubDate>Wed, 12 Aug 2015 00:00:00 +0000</pubDate>
       
       <guid>/entries/Rep_Fin_Groups.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Analysing and Comparing Encodability Criteria for Process Calculi</title>
       <link>/entries/Encodability_Process_Calculi.html</link>
       <pubDate>Mon, 10 Aug 2015 00:00:00 +0000</pubDate>
       
       <guid>/entries/Encodability_Process_Calculi.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Generating Cases from Labeled Subgoals</title>
       <link>/entries/Case_Labeling.html</link>
       <pubDate>Tue, 21 Jul 2015 00:00:00 +0000</pubDate>
       
       <guid>/entries/Case_Labeling.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Landau Symbols</title>
       <link>/entries/Landau_Symbols.html</link>
       <pubDate>Tue, 14 Jul 2015 00:00:00 +0000</pubDate>
       
       <guid>/entries/Landau_Symbols.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>The Akra-Bazzi theorem and the Master theorem</title>
       <link>/entries/Akra_Bazzi.html</link>
       <pubDate>Tue, 14 Jul 2015 00:00:00 +0000</pubDate>
       
       <guid>/entries/Akra_Bazzi.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Hermite Normal Form</title>
       <link>/entries/Hermite.html</link>
       <pubDate>Tue, 07 Jul 2015 00:00:00 +0000</pubDate>
       
       <guid>/entries/Hermite.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Derangements Formula</title>
       <link>/entries/Derangements.html</link>
       <pubDate>Sat, 27 Jun 2015 00:00:00 +0000</pubDate>
       
       <guid>/entries/Derangements.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Binary Multirelations</title>
       <link>/entries/Multirelations.html</link>
       <pubDate>Thu, 11 Jun 2015 00:00:00 +0000</pubDate>
       
       <guid>/entries/Multirelations.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Reasoning about Lists via List Interleaving</title>
       <link>/entries/List_Interleaving.html</link>
       <pubDate>Thu, 11 Jun 2015 00:00:00 +0000</pubDate>
       
       <guid>/entries/List_Interleaving.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>The Generic Unwinding Theorem for CSP Noninterference Security</title>
       <link>/entries/Noninterference_Generic_Unwinding.html</link>
       <pubDate>Thu, 11 Jun 2015 00:00:00 +0000</pubDate>
       
       <guid>/entries/Noninterference_Generic_Unwinding.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>The Ipurge Unwinding Theorem for CSP Noninterference Security</title>
       <link>/entries/Noninterference_Ipurge_Unwinding.html</link>
       <pubDate>Thu, 11 Jun 2015 00:00:00 +0000</pubDate>
       
       <guid>/entries/Noninterference_Ipurge_Unwinding.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Parameterized Dynamic Tables</title>
       <link>/entries/Dynamic_Tables.html</link>
       <pubDate>Sun, 07 Jun 2015 00:00:00 +0000</pubDate>
       
       <guid>/entries/Dynamic_Tables.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Derivatives of Logical Formulas</title>
       <link>/entries/Formula_Derivatives.html</link>
       <pubDate>Thu, 28 May 2015 00:00:00 +0000</pubDate>
       
       <guid>/entries/Formula_Derivatives.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>A Zoo of Probabilistic Systems</title>
       <link>/entries/Probabilistic_System_Zoo.html</link>
       <pubDate>Wed, 27 May 2015 00:00:00 +0000</pubDate>
       
       <guid>/entries/Probabilistic_System_Zoo.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>VCG - Combinatorial Vickrey-Clarke-Groves Auctions</title>
       <link>/entries/Vickrey_Clarke_Groves.html</link>
       <pubDate>Thu, 30 Apr 2015 00:00:00 +0000</pubDate>
       
       <guid>/entries/Vickrey_Clarke_Groves.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Residuated Lattices</title>
       <link>/entries/Residuated_Lattices.html</link>
       <pubDate>Wed, 15 Apr 2015 00:00:00 +0000</pubDate>
       
       <guid>/entries/Residuated_Lattices.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Concurrent IMP</title>
       <link>/entries/ConcurrentIMP.html</link>
       <pubDate>Mon, 13 Apr 2015 00:00:00 +0000</pubDate>
       
       <guid>/entries/ConcurrentIMP.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Relaxing Safely: Verified On-the-Fly Garbage Collection for x86-TSO</title>
       <link>/entries/ConcurrentGC.html</link>
       <pubDate>Mon, 13 Apr 2015 00:00:00 +0000</pubDate>
       
       <guid>/entries/ConcurrentGC.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Trie</title>
       <link>/entries/Trie.html</link>
       <pubDate>Mon, 30 Mar 2015 00:00:00 +0000</pubDate>
       
       <guid>/entries/Trie.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Consensus Refined</title>
       <link>/entries/Consensus_Refined.html</link>
       <pubDate>Wed, 18 Mar 2015 00:00:00 +0000</pubDate>
       
       <guid>/entries/Consensus_Refined.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Deriving class instances for datatypes</title>
       <link>/entries/Deriving.html</link>
       <pubDate>Wed, 11 Mar 2015 00:00:00 +0000</pubDate>
       
       <guid>/entries/Deriving.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>The Safety of Call Arity</title>
       <link>/entries/Call_Arity.html</link>
       <pubDate>Fri, 20 Feb 2015 00:00:00 +0000</pubDate>
       
       <guid>/entries/Call_Arity.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Echelon Form</title>
       <link>/entries/Echelon_Form.html</link>
       <pubDate>Thu, 12 Feb 2015 00:00:00 +0000</pubDate>
       
       <guid>/entries/Echelon_Form.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>QR Decomposition</title>
       <link>/entries/QR_Decomposition.html</link>
       <pubDate>Thu, 12 Feb 2015 00:00:00 +0000</pubDate>
       
       <guid>/entries/QR_Decomposition.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Finite Automata in Hereditarily Finite Set Theory</title>
       <link>/entries/Finite_Automata_HF.html</link>
       <pubDate>Thu, 05 Feb 2015 00:00:00 +0000</pubDate>
       
       <guid>/entries/Finite_Automata_HF.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Verification of the UpDown Scheme</title>
       <link>/entries/UpDown_Scheme.html</link>
       <pubDate>Wed, 28 Jan 2015 00:00:00 +0000</pubDate>
       
       <guid>/entries/UpDown_Scheme.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>The Unified Policy Framework (UPF)</title>
       <link>/entries/UPF.html</link>
       <pubDate>Fri, 28 Nov 2014 00:00:00 +0000</pubDate>
       
       <guid>/entries/UPF.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Loop freedom of the (untimed) AODV routing protocol</title>
       <link>/entries/AODV.html</link>
       <pubDate>Thu, 23 Oct 2014 00:00:00 +0000</pubDate>
       
       <guid>/entries/AODV.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Lifting Definition Option</title>
       <link>/entries/Lifting_Definition_Option.html</link>
       <pubDate>Mon, 13 Oct 2014 00:00:00 +0000</pubDate>
       
       <guid>/entries/Lifting_Definition_Option.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Stream Fusion in HOL with Code Generation</title>
       <link>/entries/Stream_Fusion_Code.html</link>
       <pubDate>Fri, 10 Oct 2014 00:00:00 +0000</pubDate>
       
       <guid>/entries/Stream_Fusion_Code.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>A Verified Compiler for Probability Density Functions</title>
       <link>/entries/Density_Compiler.html</link>
       <pubDate>Thu, 09 Oct 2014 00:00:00 +0000</pubDate>
       
       <guid>/entries/Density_Compiler.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Formalization of Refinement Calculus for Reactive Systems</title>
       <link>/entries/RefinementReactive.html</link>
       <pubDate>Wed, 08 Oct 2014 00:00:00 +0000</pubDate>
       
       <guid>/entries/RefinementReactive.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Certification Monads</title>
       <link>/entries/Certification_Monads.html</link>
       <pubDate>Fri, 03 Oct 2014 00:00:00 +0000</pubDate>
       
       <guid>/entries/Certification_Monads.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>XML</title>
       <link>/entries/XML.html</link>
       <pubDate>Fri, 03 Oct 2014 00:00:00 +0000</pubDate>
       
       <guid>/entries/XML.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Imperative Insertion Sort</title>
       <link>/entries/Imperative_Insertion_Sort.html</link>
       <pubDate>Thu, 25 Sep 2014 00:00:00 +0000</pubDate>
       
       <guid>/entries/Imperative_Insertion_Sort.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>The Sturm-Tarski Theorem</title>
       <link>/entries/Sturm_Tarski.html</link>
       <pubDate>Fri, 19 Sep 2014 00:00:00 +0000</pubDate>
       
       <guid>/entries/Sturm_Tarski.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>The Cayley-Hamilton Theorem</title>
       <link>/entries/Cayley_Hamilton.html</link>
       <pubDate>Mon, 15 Sep 2014 00:00:00 +0000</pubDate>
       
       <guid>/entries/Cayley_Hamilton.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>The Jordan-Hölder Theorem</title>
       <link>/entries/Jordan_Hoelder.html</link>
       <pubDate>Tue, 09 Sep 2014 00:00:00 +0000</pubDate>
       
       <guid>/entries/Jordan_Hoelder.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Priority Queues Based on Braun Trees</title>
       <link>/entries/Priority_Queue_Braun.html</link>
       <pubDate>Thu, 04 Sep 2014 00:00:00 +0000</pubDate>
       
       <guid>/entries/Priority_Queue_Braun.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Gauss-Jordan Algorithm and Its Applications</title>
       <link>/entries/Gauss_Jordan.html</link>
       <pubDate>Wed, 03 Sep 2014 00:00:00 +0000</pubDate>
       
       <guid>/entries/Gauss_Jordan.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Real-Valued Special Functions: Upper and Lower Bounds</title>
       <link>/entries/Special_Function_Bounds.html</link>
       <pubDate>Fri, 29 Aug 2014 00:00:00 +0000</pubDate>
       
       <guid>/entries/Special_Function_Bounds.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Vector Spaces</title>
       <link>/entries/VectorSpace.html</link>
       <pubDate>Fri, 29 Aug 2014 00:00:00 +0000</pubDate>
       
       <guid>/entries/VectorSpace.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Skew Heap</title>
       <link>/entries/Skew_Heap.html</link>
       <pubDate>Wed, 13 Aug 2014 00:00:00 +0000</pubDate>
       
       <guid>/entries/Skew_Heap.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Splay Tree</title>
       <link>/entries/Splay_Tree.html</link>
       <pubDate>Tue, 12 Aug 2014 00:00:00 +0000</pubDate>
       
       <guid>/entries/Splay_Tree.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Haskell&#39;s Show Class in Isabelle/HOL</title>
       <link>/entries/Show.html</link>
       <pubDate>Tue, 29 Jul 2014 00:00:00 +0000</pubDate>
       
       <guid>/entries/Show.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Formal Specification of a Generic Separation Kernel</title>
       <link>/entries/CISC-Kernel.html</link>
       <pubDate>Fri, 18 Jul 2014 00:00:00 +0000</pubDate>
       
       <guid>/entries/CISC-Kernel.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>pGCL for Isabelle</title>
       <link>/entries/pGCL.html</link>
       <pubDate>Sun, 13 Jul 2014 00:00:00 +0000</pubDate>
       
       <guid>/entries/pGCL.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Amortized Complexity Verified</title>
       <link>/entries/Amortized_Complexity.html</link>
       <pubDate>Mon, 07 Jul 2014 00:00:00 +0000</pubDate>
       
       <guid>/entries/Amortized_Complexity.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Network Security Policy Verification</title>
       <link>/entries/Network_Security_Policy_Verification.html</link>
       <pubDate>Fri, 04 Jul 2014 00:00:00 +0000</pubDate>
       
       <guid>/entries/Network_Security_Policy_Verification.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Pop-Refinement</title>
       <link>/entries/Pop_Refinement.html</link>
       <pubDate>Thu, 03 Jul 2014 00:00:00 +0000</pubDate>
       
       <guid>/entries/Pop_Refinement.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Decision Procedures for MSO on Words Based on Derivatives of Regular Expressions</title>
       <link>/entries/MSO_Regex_Equivalence.html</link>
       <pubDate>Thu, 12 Jun 2014 00:00:00 +0000</pubDate>
       
       <guid>/entries/MSO_Regex_Equivalence.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Boolean Expression Checkers</title>
       <link>/entries/Boolean_Expression_Checkers.html</link>
       <pubDate>Sun, 08 Jun 2014 00:00:00 +0000</pubDate>
       
       <guid>/entries/Boolean_Expression_Checkers.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>A Fully Verified Executable LTL Model Checker</title>
       <link>/entries/CAVA_LTL_Modelchecker.html</link>
       <pubDate>Wed, 28 May 2014 00:00:00 +0000</pubDate>
       
       <guid>/entries/CAVA_LTL_Modelchecker.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Converting Linear-Time Temporal Logic to Generalized Büchi Automata</title>
       <link>/entries/LTL_to_GBA.html</link>
       <pubDate>Wed, 28 May 2014 00:00:00 +0000</pubDate>
       
       <guid>/entries/LTL_to_GBA.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Promela Formalization</title>
       <link>/entries/Promela.html</link>
       <pubDate>Wed, 28 May 2014 00:00:00 +0000</pubDate>
       
       <guid>/entries/Promela.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>The CAVA Automata Library</title>
       <link>/entries/CAVA_Automata.html</link>
       <pubDate>Wed, 28 May 2014 00:00:00 +0000</pubDate>
       
       <guid>/entries/CAVA_Automata.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Verified Efficient Implementation of Gabow&#39;s Strongly Connected Components Algorithm</title>
       <link>/entries/Gabow_SCC.html</link>
       <pubDate>Wed, 28 May 2014 00:00:00 +0000</pubDate>
       
       <guid>/entries/Gabow_SCC.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Noninterference Security in Communicating Sequential Processes</title>
       <link>/entries/Noninterference_CSP.html</link>
       <pubDate>Fri, 23 May 2014 00:00:00 +0000</pubDate>
       
       <guid>/entries/Noninterference_CSP.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Transitive closure according to Roy-Floyd-Warshall</title>
       <link>/entries/Roy_Floyd_Warshall.html</link>
       <pubDate>Fri, 23 May 2014 00:00:00 +0000</pubDate>
       
       <guid>/entries/Roy_Floyd_Warshall.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Regular Algebras</title>
       <link>/entries/Regular_Algebras.html</link>
       <pubDate>Wed, 21 May 2014 00:00:00 +0000</pubDate>
       
       <guid>/entries/Regular_Algebras.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Formalisation and Analysis of Component Dependencies</title>
       <link>/entries/ComponentDependencies.html</link>
       <pubDate>Mon, 28 Apr 2014 00:00:00 +0000</pubDate>
       
       <guid>/entries/ComponentDependencies.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>A Formalization of Assumptions and Guarantees for Compositional Noninterference</title>
       <link>/entries/SIFUM_Type_Systems.html</link>
       <pubDate>Wed, 23 Apr 2014 00:00:00 +0000</pubDate>
       
       <guid>/entries/SIFUM_Type_Systems.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>A Formalization of Declassification with WHAT-and-WHERE-Security</title>
       <link>/entries/WHATandWHERE_Security.html</link>
       <pubDate>Wed, 23 Apr 2014 00:00:00 +0000</pubDate>
       
       <guid>/entries/WHATandWHERE_Security.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>A Formalization of Strong Security</title>
       <link>/entries/Strong_Security.html</link>
       <pubDate>Wed, 23 Apr 2014 00:00:00 +0000</pubDate>
       
       <guid>/entries/Strong_Security.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Bounded-Deducibility Security</title>
       <link>/entries/Bounded_Deducibility_Security.html</link>
       <pubDate>Tue, 22 Apr 2014 00:00:00 +0000</pubDate>
       
       <guid>/entries/Bounded_Deducibility_Security.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>A shallow embedding of HyperCTL*</title>
       <link>/entries/HyperCTL.html</link>
       <pubDate>Wed, 16 Apr 2014 00:00:00 +0000</pubDate>
       
       <guid>/entries/HyperCTL.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Abstract Completeness</title>
       <link>/entries/Abstract_Completeness.html</link>
       <pubDate>Wed, 16 Apr 2014 00:00:00 +0000</pubDate>
       
       <guid>/entries/Abstract_Completeness.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Discrete Summation</title>
       <link>/entries/Discrete_Summation.html</link>
       <pubDate>Sun, 13 Apr 2014 00:00:00 +0000</pubDate>
       
       <guid>/entries/Discrete_Summation.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Syntax and semantics of a GPU kernel programming language</title>
       <link>/entries/GPU_Kernel_PL.html</link>
       <pubDate>Thu, 03 Apr 2014 00:00:00 +0000</pubDate>
       
       <guid>/entries/GPU_Kernel_PL.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Probabilistic Noninterference</title>
       <link>/entries/Probabilistic_Noninterference.html</link>
       <pubDate>Tue, 11 Mar 2014 00:00:00 +0000</pubDate>
       
       <guid>/entries/Probabilistic_Noninterference.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Mechanization of the Algebra for Wireless Networks (AWN)</title>
       <link>/entries/AWN.html</link>
       <pubDate>Sat, 08 Mar 2014 00:00:00 +0000</pubDate>
       
       <guid>/entries/AWN.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Mutually Recursive Partial Functions</title>
       <link>/entries/Partial_Function_MR.html</link>
       <pubDate>Tue, 18 Feb 2014 00:00:00 +0000</pubDate>
       
       <guid>/entries/Partial_Function_MR.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Properties of Random Graphs -- Subgraph Containment</title>
       <link>/entries/Random_Graph_Subgraph_Threshold.html</link>
       <pubDate>Thu, 13 Feb 2014 00:00:00 +0000</pubDate>
       
       <guid>/entries/Random_Graph_Subgraph_Threshold.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Verification of Selection and Heap Sort Using Locales</title>
       <link>/entries/Selection_Heap_Sort.html</link>
       <pubDate>Tue, 11 Feb 2014 00:00:00 +0000</pubDate>
       
       <guid>/entries/Selection_Heap_Sort.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Affine Arithmetic</title>
       <link>/entries/Affine_Arithmetic.html</link>
       <pubDate>Fri, 07 Feb 2014 00:00:00 +0000</pubDate>
       
       <guid>/entries/Affine_Arithmetic.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Implementing field extensions of the form Q[sqrt(b)]</title>
       <link>/entries/Real_Impl.html</link>
       <pubDate>Thu, 06 Feb 2014 00:00:00 +0000</pubDate>
       
       <guid>/entries/Real_Impl.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Unified Decision Procedures for Regular Expression Equivalence</title>
       <link>/entries/Regex_Equivalence.html</link>
       <pubDate>Thu, 30 Jan 2014 00:00:00 +0000</pubDate>
       
       <guid>/entries/Regex_Equivalence.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Secondary Sylow Theorems</title>
       <link>/entries/Secondary_Sylow.html</link>
       <pubDate>Tue, 28 Jan 2014 00:00:00 +0000</pubDate>
       
       <guid>/entries/Secondary_Sylow.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Relation Algebra</title>
       <link>/entries/Relation_Algebra.html</link>
       <pubDate>Sat, 25 Jan 2014 00:00:00 +0000</pubDate>
       
       <guid>/entries/Relation_Algebra.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Kleene Algebra with Tests and Demonic Refinement Algebras</title>
       <link>/entries/KAT_and_DRA.html</link>
       <pubDate>Thu, 23 Jan 2014 00:00:00 +0000</pubDate>
       
       <guid>/entries/KAT_and_DRA.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Featherweight OCL: A Proposal for a Machine-Checked Formal Semantics for OCL 2.5</title>
       <link>/entries/Featherweight_OCL.html</link>
       <pubDate>Thu, 16 Jan 2014 00:00:00 +0000</pubDate>
       
       <guid>/entries/Featherweight_OCL.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Compositional Properties of Crypto-Based Components</title>
       <link>/entries/CryptoBasedCompositionalProperties.html</link>
       <pubDate>Sat, 11 Jan 2014 00:00:00 +0000</pubDate>
       
       <guid>/entries/CryptoBasedCompositionalProperties.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Sturm&#39;s Theorem</title>
       <link>/entries/Sturm_Sequences.html</link>
       <pubDate>Sat, 11 Jan 2014 00:00:00 +0000</pubDate>
       
       <guid>/entries/Sturm_Sequences.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>A General Method for the Proof of Theorems on Tail-recursive Functions</title>
       <link>/entries/Tail_Recursive_Functions.html</link>
       <pubDate>Sun, 01 Dec 2013 00:00:00 +0000</pubDate>
       
       <guid>/entries/Tail_Recursive_Functions.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Gödel&#39;s Incompleteness Theorems</title>
       <link>/entries/Incompleteness.html</link>
       <pubDate>Sun, 17 Nov 2013 00:00:00 +0000</pubDate>
       
       <guid>/entries/Incompleteness.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>The Hereditarily Finite Sets</title>
       <link>/entries/HereditarilyFinite.html</link>
       <pubDate>Sun, 17 Nov 2013 00:00:00 +0000</pubDate>
       
       <guid>/entries/HereditarilyFinite.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>A Codatatype of Formal Languages</title>
       <link>/entries/Coinductive_Languages.html</link>
       <pubDate>Fri, 15 Nov 2013 00:00:00 +0000</pubDate>
       
       <guid>/entries/Coinductive_Languages.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Stream Processing Components: Isabelle/HOL Formalisation and Case Studies</title>
       <link>/entries/FocusStreamsCaseStudies.html</link>
       <pubDate>Thu, 14 Nov 2013 00:00:00 +0000</pubDate>
       
       <guid>/entries/FocusStreamsCaseStudies.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Gödel&#39;s God in Isabelle/HOL</title>
       <link>/entries/GoedelGod.html</link>
       <pubDate>Tue, 12 Nov 2013 00:00:00 +0000</pubDate>
       
       <guid>/entries/GoedelGod.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Decreasing Diagrams</title>
       <link>/entries/Decreasing-Diagrams.html</link>
       <pubDate>Fri, 01 Nov 2013 00:00:00 +0000</pubDate>
       
       <guid>/entries/Decreasing-Diagrams.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Automatic Data Refinement</title>
       <link>/entries/Automatic_Refinement.html</link>
       <pubDate>Wed, 02 Oct 2013 00:00:00 +0000</pubDate>
       
       <guid>/entries/Automatic_Refinement.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Native Word</title>
       <link>/entries/Native_Word.html</link>
       <pubDate>Tue, 17 Sep 2013 00:00:00 +0000</pubDate>
       
       <guid>/entries/Native_Word.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>A Formal Model of IEEE Floating Point Arithmetic</title>
       <link>/entries/IEEE_Floating_Point.html</link>
       <pubDate>Sat, 27 Jul 2013 00:00:00 +0000</pubDate>
       
       <guid>/entries/IEEE_Floating_Point.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Lehmer&#39;s Theorem</title>
       <link>/entries/Lehmer.html</link>
       <pubDate>Mon, 22 Jul 2013 00:00:00 +0000</pubDate>
       
       <guid>/entries/Lehmer.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Pratt&#39;s Primality Certificates</title>
       <link>/entries/Pratt_Certificate.html</link>
       <pubDate>Mon, 22 Jul 2013 00:00:00 +0000</pubDate>
       
       <guid>/entries/Pratt_Certificate.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>The Königsberg Bridge Problem and the Friendship Theorem</title>
       <link>/entries/Koenigsberg_Friendship.html</link>
       <pubDate>Fri, 19 Jul 2013 00:00:00 +0000</pubDate>
       
       <guid>/entries/Koenigsberg_Friendship.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Sound and Complete Sort Encodings for First-Order Logic</title>
       <link>/entries/Sort_Encodings.html</link>
       <pubDate>Thu, 27 Jun 2013 00:00:00 +0000</pubDate>
       
       <guid>/entries/Sort_Encodings.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>An Axiomatic Characterization of the Single-Source Shortest Path Problem</title>
       <link>/entries/ShortestPath.html</link>
       <pubDate>Wed, 22 May 2013 00:00:00 +0000</pubDate>
       
       <guid>/entries/ShortestPath.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Graph Theory</title>
       <link>/entries/Graph_Theory.html</link>
       <pubDate>Sun, 28 Apr 2013 00:00:00 +0000</pubDate>
       
       <guid>/entries/Graph_Theory.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Light-weight Containers</title>
       <link>/entries/Containers.html</link>
       <pubDate>Mon, 15 Apr 2013 00:00:00 +0000</pubDate>
       
       <guid>/entries/Containers.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Nominal 2</title>
       <link>/entries/Nominal2.html</link>
       <pubDate>Thu, 21 Feb 2013 00:00:00 +0000</pubDate>
       
       <guid>/entries/Nominal2.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>The Correctness of Launchbury&#39;s Natural Semantics for Lazy Evaluation</title>
       <link>/entries/Launchbury.html</link>
       <pubDate>Thu, 31 Jan 2013 00:00:00 +0000</pubDate>
       
       <guid>/entries/Launchbury.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Ribbon Proofs</title>
       <link>/entries/Ribbon_Proofs.html</link>
       <pubDate>Sat, 19 Jan 2013 00:00:00 +0000</pubDate>
       
       <guid>/entries/Ribbon_Proofs.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Rank-Nullity Theorem in Linear Algebra</title>
       <link>/entries/Rank_Nullity_Theorem.html</link>
       <pubDate>Wed, 16 Jan 2013 00:00:00 +0000</pubDate>
       
       <guid>/entries/Rank_Nullity_Theorem.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Kleene Algebra</title>
       <link>/entries/Kleene_Algebra.html</link>
       <pubDate>Tue, 15 Jan 2013 00:00:00 +0000</pubDate>
       
       <guid>/entries/Kleene_Algebra.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Computing N-th Roots using the Babylonian Method</title>
       <link>/entries/Sqrt_Babylonian.html</link>
       <pubDate>Thu, 03 Jan 2013 00:00:00 +0000</pubDate>
       
       <guid>/entries/Sqrt_Babylonian.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>A Separation Logic Framework for Imperative HOL</title>
       <link>/entries/Separation_Logic_Imperative_HOL.html</link>
       <pubDate>Wed, 14 Nov 2012 00:00:00 +0000</pubDate>
       
       <guid>/entries/Separation_Logic_Imperative_HOL.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Open Induction</title>
       <link>/entries/Open_Induction.html</link>
       <pubDate>Fri, 02 Nov 2012 00:00:00 +0000</pubDate>
       
       <guid>/entries/Open_Induction.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>The independence of Tarski&#39;s Euclidean axiom</title>
       <link>/entries/Tarskis_Geometry.html</link>
       <pubDate>Tue, 30 Oct 2012 00:00:00 +0000</pubDate>
       
       <guid>/entries/Tarskis_Geometry.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Bondy&#39;s Theorem</title>
       <link>/entries/Bondy.html</link>
       <pubDate>Sat, 27 Oct 2012 00:00:00 +0000</pubDate>
       
       <guid>/entries/Bondy.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Possibilistic Noninterference</title>
       <link>/entries/Possibilistic_Noninterference.html</link>
       <pubDate>Mon, 10 Sep 2012 00:00:00 +0000</pubDate>
       
       <guid>/entries/Possibilistic_Noninterference.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Generating linear orders for datatypes</title>
       <link>/entries/Datatype_Order_Generator.html</link>
       <pubDate>Tue, 07 Aug 2012 00:00:00 +0000</pubDate>
       
       <guid>/entries/Datatype_Order_Generator.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Proving the Impossibility of Trisecting an Angle and Doubling the Cube</title>
       <link>/entries/Impossible_Geometry.html</link>
       <pubDate>Sun, 05 Aug 2012 00:00:00 +0000</pubDate>
       
       <guid>/entries/Impossible_Geometry.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Verifying Fault-Tolerant Distributed Algorithms in the Heard-Of Model</title>
       <link>/entries/Heard_Of.html</link>
       <pubDate>Fri, 27 Jul 2012 00:00:00 +0000</pubDate>
       
       <guid>/entries/Heard_Of.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Logical Relations for PCF</title>
       <link>/entries/PCF.html</link>
       <pubDate>Sun, 01 Jul 2012 00:00:00 +0000</pubDate>
       
       <guid>/entries/PCF.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Type Constructor Classes and Monad Transformers</title>
       <link>/entries/Tycon.html</link>
       <pubDate>Tue, 26 Jun 2012 00:00:00 +0000</pubDate>
       
       <guid>/entries/Tycon.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>CCS in nominal logic</title>
       <link>/entries/CCS.html</link>
       <pubDate>Tue, 29 May 2012 00:00:00 +0000</pubDate>
       
       <guid>/entries/CCS.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Psi-calculi in Isabelle</title>
       <link>/entries/Psi_Calculi.html</link>
       <pubDate>Tue, 29 May 2012 00:00:00 +0000</pubDate>
       
       <guid>/entries/Psi_Calculi.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>The pi-calculus in nominal logic</title>
       <link>/entries/Pi_Calculus.html</link>
       <pubDate>Tue, 29 May 2012 00:00:00 +0000</pubDate>
       
       <guid>/entries/Pi_Calculus.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Isabelle/Circus</title>
       <link>/entries/Circus.html</link>
       <pubDate>Sun, 27 May 2012 00:00:00 +0000</pubDate>
       
       <guid>/entries/Circus.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Separation Algebra</title>
       <link>/entries/Separation_Algebra.html</link>
       <pubDate>Fri, 11 May 2012 00:00:00 +0000</pubDate>
       
       <guid>/entries/Separation_Algebra.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Stuttering Equivalence</title>
       <link>/entries/Stuttering_Equivalence.html</link>
       <pubDate>Mon, 07 May 2012 00:00:00 +0000</pubDate>
       
       <guid>/entries/Stuttering_Equivalence.html</guid>
       <description></description>
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     <item>
       <title>Inductive Study of Confidentiality</title>
       <link>/entries/Inductive_Confidentiality.html</link>
       <pubDate>Wed, 02 May 2012 00:00:00 +0000</pubDate>
       
       <guid>/entries/Inductive_Confidentiality.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Ordinary Differential Equations</title>
       <link>/entries/Ordinary_Differential_Equations.html</link>
       <pubDate>Thu, 26 Apr 2012 00:00:00 +0000</pubDate>
       
       <guid>/entries/Ordinary_Differential_Equations.html</guid>
       <description></description>
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     <item>
       <title>Well-Quasi-Orders</title>
       <link>/entries/Well_Quasi_Orders.html</link>
       <pubDate>Fri, 13 Apr 2012 00:00:00 +0000</pubDate>
       
       <guid>/entries/Well_Quasi_Orders.html</guid>
       <description></description>
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     <item>
       <title>Abortable Linearizable Modules</title>
       <link>/entries/Abortable_Linearizable_Modules.html</link>
       <pubDate>Thu, 01 Mar 2012 00:00:00 +0000</pubDate>
       
       <guid>/entries/Abortable_Linearizable_Modules.html</guid>
       <description></description>
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     <item>
       <title>Executable Transitive Closures</title>
       <link>/entries/Transitive-Closure-II.html</link>
       <pubDate>Wed, 29 Feb 2012 00:00:00 +0000</pubDate>
       
       <guid>/entries/Transitive-Closure-II.html</guid>
       <description></description>
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     <item>
       <title>A Probabilistic Proof of the Girth-Chromatic Number Theorem</title>
       <link>/entries/Girth_Chromatic.html</link>
       <pubDate>Mon, 06 Feb 2012 00:00:00 +0000</pubDate>
       
       <guid>/entries/Girth_Chromatic.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Dijkstra&#39;s Shortest Path Algorithm</title>
       <link>/entries/Dijkstra_Shortest_Path.html</link>
       <pubDate>Mon, 30 Jan 2012 00:00:00 +0000</pubDate>
       
       <guid>/entries/Dijkstra_Shortest_Path.html</guid>
       <description></description>
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     <item>
       <title>Refinement for Monadic Programs</title>
       <link>/entries/Refine_Monadic.html</link>
       <pubDate>Mon, 30 Jan 2012 00:00:00 +0000</pubDate>
       
       <guid>/entries/Refine_Monadic.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Markov Models</title>
       <link>/entries/Markov_Models.html</link>
       <pubDate>Tue, 03 Jan 2012 00:00:00 +0000</pubDate>
       
       <guid>/entries/Markov_Models.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>A Definitional Encoding of TLA* in Isabelle/HOL</title>
       <link>/entries/TLA.html</link>
       <pubDate>Sat, 19 Nov 2011 00:00:00 +0000</pubDate>
       
       <guid>/entries/TLA.html</guid>
       <description></description>
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     <item>
       <title>Efficient Mergesort</title>
       <link>/entries/Efficient-Mergesort.html</link>
       <pubDate>Wed, 09 Nov 2011 00:00:00 +0000</pubDate>
       
       <guid>/entries/Efficient-Mergesort.html</guid>
       <description></description>
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     <item>
       <title>Algebra of Monotonic Boolean Transformers</title>
       <link>/entries/MonoBoolTranAlgebra.html</link>
       <pubDate>Thu, 22 Sep 2011 00:00:00 +0000</pubDate>
       
       <guid>/entries/MonoBoolTranAlgebra.html</guid>
       <description></description>
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     <item>
       <title>Lattice Properties</title>
       <link>/entries/LatticeProperties.html</link>
       <pubDate>Thu, 22 Sep 2011 00:00:00 +0000</pubDate>
       
       <guid>/entries/LatticeProperties.html</guid>
       <description></description>
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     <item>
       <title>Pseudo Hoops</title>
       <link>/entries/PseudoHoops.html</link>
       <pubDate>Thu, 22 Sep 2011 00:00:00 +0000</pubDate>
       
       <guid>/entries/PseudoHoops.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>The Myhill-Nerode Theorem Based on Regular Expressions</title>
       <link>/entries/Myhill-Nerode.html</link>
       <pubDate>Fri, 26 Aug 2011 00:00:00 +0000</pubDate>
       
       <guid>/entries/Myhill-Nerode.html</guid>
       <description></description>
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     <item>
       <title>Gauss-Jordan Elimination for Matrices Represented as Functions</title>
       <link>/entries/Gauss-Jordan-Elim-Fun.html</link>
       <pubDate>Fri, 19 Aug 2011 00:00:00 +0000</pubDate>
       
       <guid>/entries/Gauss-Jordan-Elim-Fun.html</guid>
       <description></description>
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     <item>
       <title>Maximum Cardinality Matching</title>
       <link>/entries/Max-Card-Matching.html</link>
       <pubDate>Thu, 21 Jul 2011 00:00:00 +0000</pubDate>
       
       <guid>/entries/Max-Card-Matching.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Knowledge-based programs</title>
       <link>/entries/KBPs.html</link>
       <pubDate>Tue, 17 May 2011 00:00:00 +0000</pubDate>
       
       <guid>/entries/KBPs.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>The General Triangle Is Unique</title>
       <link>/entries/General-Triangle.html</link>
       <pubDate>Fri, 01 Apr 2011 00:00:00 +0000</pubDate>
       
       <guid>/entries/General-Triangle.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Executable Transitive Closures of Finite Relations</title>
       <link>/entries/Transitive-Closure.html</link>
       <pubDate>Mon, 14 Mar 2011 00:00:00 +0000</pubDate>
       
       <guid>/entries/Transitive-Closure.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>AutoFocus Stream Processing for Single-Clocking and Multi-Clocking Semantics</title>
       <link>/entries/AutoFocus-Stream.html</link>
       <pubDate>Wed, 23 Feb 2011 00:00:00 +0000</pubDate>
       
       <guid>/entries/AutoFocus-Stream.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Infinite Lists</title>
       <link>/entries/List-Infinite.html</link>
       <pubDate>Wed, 23 Feb 2011 00:00:00 +0000</pubDate>
       
       <guid>/entries/List-Infinite.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Interval Temporal Logic on Natural Numbers</title>
       <link>/entries/Nat-Interval-Logic.html</link>
       <pubDate>Wed, 23 Feb 2011 00:00:00 +0000</pubDate>
       
       <guid>/entries/Nat-Interval-Logic.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Lightweight Java</title>
       <link>/entries/LightweightJava.html</link>
       <pubDate>Mon, 07 Feb 2011 00:00:00 +0000</pubDate>
       
       <guid>/entries/LightweightJava.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>RIPEMD-160</title>
       <link>/entries/RIPEMD-160-SPARK.html</link>
       <pubDate>Mon, 10 Jan 2011 00:00:00 +0000</pubDate>
       
       <guid>/entries/RIPEMD-160-SPARK.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Lower Semicontinuous Functions</title>
       <link>/entries/Lower_Semicontinuous.html</link>
       <pubDate>Sat, 08 Jan 2011 00:00:00 +0000</pubDate>
       
       <guid>/entries/Lower_Semicontinuous.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Hall&#39;s Marriage Theorem</title>
       <link>/entries/Marriage.html</link>
       <pubDate>Fri, 17 Dec 2010 00:00:00 +0000</pubDate>
       
       <guid>/entries/Marriage.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Shivers&#39; Control Flow Analysis</title>
       <link>/entries/Shivers-CFA.html</link>
       <pubDate>Tue, 16 Nov 2010 00:00:00 +0000</pubDate>
       
       <guid>/entries/Shivers-CFA.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Binomial Heaps and Skew Binomial Heaps</title>
       <link>/entries/Binomial-Heaps.html</link>
       <pubDate>Thu, 28 Oct 2010 00:00:00 +0000</pubDate>
       
       <guid>/entries/Binomial-Heaps.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Finger Trees</title>
       <link>/entries/Finger-Trees.html</link>
       <pubDate>Thu, 28 Oct 2010 00:00:00 +0000</pubDate>
       
       <guid>/entries/Finger-Trees.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Functional Binomial Queues</title>
       <link>/entries/Binomial-Queues.html</link>
       <pubDate>Thu, 28 Oct 2010 00:00:00 +0000</pubDate>
       
       <guid>/entries/Binomial-Queues.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Strong Normalization of Moggis&#39;s Computational Metalanguage</title>
       <link>/entries/Lam-ml-Normalization.html</link>
       <pubDate>Sun, 29 Aug 2010 00:00:00 +0000</pubDate>
       
       <guid>/entries/Lam-ml-Normalization.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Executable Multivariate Polynomials</title>
       <link>/entries/Polynomials.html</link>
       <pubDate>Tue, 10 Aug 2010 00:00:00 +0000</pubDate>
       
       <guid>/entries/Polynomials.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Formalizing Statecharts using Hierarchical Automata</title>
       <link>/entries/Statecharts.html</link>
       <pubDate>Sun, 08 Aug 2010 00:00:00 +0000</pubDate>
       
       <guid>/entries/Statecharts.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Free Groups</title>
       <link>/entries/Free-Groups.html</link>
       <pubDate>Thu, 24 Jun 2010 00:00:00 +0000</pubDate>
       
       <guid>/entries/Free-Groups.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Category Theory</title>
       <link>/entries/Category2.html</link>
       <pubDate>Sun, 20 Jun 2010 00:00:00 +0000</pubDate>
       
       <guid>/entries/Category2.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Executable Matrix Operations on Matrices of Arbitrary Dimensions</title>
       <link>/entries/Matrix.html</link>
       <pubDate>Thu, 17 Jun 2010 00:00:00 +0000</pubDate>
       
       <guid>/entries/Matrix.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Abstract Rewriting</title>
       <link>/entries/Abstract-Rewriting.html</link>
       <pubDate>Mon, 14 Jun 2010 00:00:00 +0000</pubDate>
       
       <guid>/entries/Abstract-Rewriting.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Semantics and Data Refinement of Invariant Based Programs</title>
       <link>/entries/DataRefinementIBP.html</link>
       <pubDate>Fri, 28 May 2010 00:00:00 +0000</pubDate>
       
       <guid>/entries/DataRefinementIBP.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Verification of the Deutsch-Schorr-Waite Graph Marking Algorithm using Data Refinement</title>
       <link>/entries/GraphMarkingIBP.html</link>
       <pubDate>Fri, 28 May 2010 00:00:00 +0000</pubDate>
       
       <guid>/entries/GraphMarkingIBP.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>A Complete Proof of the Robbins Conjecture</title>
       <link>/entries/Robbins-Conjecture.html</link>
       <pubDate>Sat, 22 May 2010 00:00:00 +0000</pubDate>
       
       <guid>/entries/Robbins-Conjecture.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Regular Sets and Expressions</title>
       <link>/entries/Regular-Sets.html</link>
       <pubDate>Wed, 12 May 2010 00:00:00 +0000</pubDate>
       
       <guid>/entries/Regular-Sets.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Locally Nameless Sigma Calculus</title>
       <link>/entries/Locally-Nameless-Sigma.html</link>
       <pubDate>Fri, 30 Apr 2010 00:00:00 +0000</pubDate>
       
       <guid>/entries/Locally-Nameless-Sigma.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Free Boolean Algebra</title>
       <link>/entries/Free-Boolean-Algebra.html</link>
       <pubDate>Mon, 29 Mar 2010 00:00:00 +0000</pubDate>
       
       <guid>/entries/Free-Boolean-Algebra.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Information Flow Noninterference via Slicing</title>
       <link>/entries/InformationFlowSlicing.html</link>
       <pubDate>Tue, 23 Mar 2010 00:00:00 +0000</pubDate>
       
       <guid>/entries/InformationFlowSlicing.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Inter-Procedural Information Flow Noninterference via Slicing</title>
       <link>/entries/InformationFlowSlicing_Inter.html</link>
       <pubDate>Tue, 23 Mar 2010 00:00:00 +0000</pubDate>
       
       <guid>/entries/InformationFlowSlicing_Inter.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>List Index</title>
       <link>/entries/List-Index.html</link>
       <pubDate>Sat, 20 Feb 2010 00:00:00 +0000</pubDate>
       
       <guid>/entries/List-Index.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Coinductive</title>
       <link>/entries/Coinductive.html</link>
       <pubDate>Fri, 12 Feb 2010 00:00:00 +0000</pubDate>
       
       <guid>/entries/Coinductive.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>A Fast SAT Solver for Isabelle in Standard ML</title>
       <link>/entries/DPT-SAT-Solver.html</link>
       <pubDate>Wed, 09 Dec 2009 00:00:00 +0000</pubDate>
       
       <guid>/entries/DPT-SAT-Solver.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Formalizing the Logic-Automaton Connection</title>
       <link>/entries/Presburger-Automata.html</link>
       <pubDate>Thu, 03 Dec 2009 00:00:00 +0000</pubDate>
       
       <guid>/entries/Presburger-Automata.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Collections Framework</title>
       <link>/entries/Collections.html</link>
       <pubDate>Wed, 25 Nov 2009 00:00:00 +0000</pubDate>
       
       <guid>/entries/Collections.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Tree Automata</title>
       <link>/entries/Tree-Automata.html</link>
       <pubDate>Wed, 25 Nov 2009 00:00:00 +0000</pubDate>
       
       <guid>/entries/Tree-Automata.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Perfect Number Theorem</title>
       <link>/entries/Perfect-Number-Thm.html</link>
       <pubDate>Sun, 22 Nov 2009 00:00:00 +0000</pubDate>
       
       <guid>/entries/Perfect-Number-Thm.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Backing up Slicing: Verifying the Interprocedural Two-Phase Horwitz-Reps-Binkley Slicer</title>
       <link>/entries/HRB-Slicing.html</link>
       <pubDate>Fri, 13 Nov 2009 00:00:00 +0000</pubDate>
       
       <guid>/entries/HRB-Slicing.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>The Worker/Wrapper Transformation</title>
       <link>/entries/WorkerWrapper.html</link>
       <pubDate>Fri, 30 Oct 2009 00:00:00 +0000</pubDate>
       
       <guid>/entries/WorkerWrapper.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Ordinals and Cardinals</title>
       <link>/entries/Ordinals_and_Cardinals.html</link>
       <pubDate>Tue, 01 Sep 2009 00:00:00 +0000</pubDate>
       
       <guid>/entries/Ordinals_and_Cardinals.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Invertibility in Sequent Calculi</title>
       <link>/entries/SequentInvertibility.html</link>
       <pubDate>Fri, 28 Aug 2009 00:00:00 +0000</pubDate>
       
       <guid>/entries/SequentInvertibility.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>An Example of a Cofinitary Group in Isabelle/HOL</title>
       <link>/entries/CofGroups.html</link>
       <pubDate>Tue, 04 Aug 2009 00:00:00 +0000</pubDate>
       
       <guid>/entries/CofGroups.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Code Generation for Functions as Data</title>
       <link>/entries/FinFun.html</link>
       <pubDate>Wed, 06 May 2009 00:00:00 +0000</pubDate>
       
       <guid>/entries/FinFun.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Stream Fusion</title>
       <link>/entries/Stream-Fusion.html</link>
       <pubDate>Wed, 29 Apr 2009 00:00:00 +0000</pubDate>
       
       <guid>/entries/Stream-Fusion.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>A Bytecode Logic for JML and Types</title>
       <link>/entries/BytecodeLogicJmlTypes.html</link>
       <pubDate>Fri, 12 Dec 2008 00:00:00 +0000</pubDate>
       
       <guid>/entries/BytecodeLogicJmlTypes.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Secure information flow and program logics</title>
       <link>/entries/SIFPL.html</link>
       <pubDate>Mon, 10 Nov 2008 00:00:00 +0000</pubDate>
       
       <guid>/entries/SIFPL.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Some classical results in Social Choice Theory</title>
       <link>/entries/SenSocialChoice.html</link>
       <pubDate>Sun, 09 Nov 2008 00:00:00 +0000</pubDate>
       
       <guid>/entries/SenSocialChoice.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Fun With Tilings</title>
       <link>/entries/FunWithTilings.html</link>
       <pubDate>Fri, 07 Nov 2008 00:00:00 +0000</pubDate>
       
       <guid>/entries/FunWithTilings.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>The Textbook Proof of Huffman&#39;s Algorithm</title>
       <link>/entries/Huffman.html</link>
       <pubDate>Wed, 15 Oct 2008 00:00:00 +0000</pubDate>
       
       <guid>/entries/Huffman.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Towards Certified Slicing</title>
       <link>/entries/Slicing.html</link>
       <pubDate>Tue, 16 Sep 2008 00:00:00 +0000</pubDate>
       
       <guid>/entries/Slicing.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>A Correctness Proof for the Volpano/Smith Security Typing System</title>
       <link>/entries/VolpanoSmith.html</link>
       <pubDate>Tue, 02 Sep 2008 00:00:00 +0000</pubDate>
       
       <guid>/entries/VolpanoSmith.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Arrow and Gibbard-Satterthwaite</title>
       <link>/entries/ArrowImpossibilityGS.html</link>
       <pubDate>Mon, 01 Sep 2008 00:00:00 +0000</pubDate>
       
       <guid>/entries/ArrowImpossibilityGS.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Fun With Functions</title>
       <link>/entries/FunWithFunctions.html</link>
       <pubDate>Tue, 26 Aug 2008 00:00:00 +0000</pubDate>
       
       <guid>/entries/FunWithFunctions.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Formal Verification of Modern SAT Solvers</title>
       <link>/entries/SATSolverVerification.html</link>
       <pubDate>Wed, 23 Jul 2008 00:00:00 +0000</pubDate>
       
       <guid>/entries/SATSolverVerification.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Recursion Theory I</title>
       <link>/entries/Recursion-Theory-I.html</link>
       <pubDate>Sat, 05 Apr 2008 00:00:00 +0000</pubDate>
       
       <guid>/entries/Recursion-Theory-I.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>A Sequential Imperative Programming Language Syntax, Semantics, Hoare Logics and Verification Environment</title>
       <link>/entries/Simpl.html</link>
       <pubDate>Fri, 29 Feb 2008 00:00:00 +0000</pubDate>
       
       <guid>/entries/Simpl.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>BDD Normalisation</title>
       <link>/entries/BDD.html</link>
       <pubDate>Fri, 29 Feb 2008 00:00:00 +0000</pubDate>
       
       <guid>/entries/BDD.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Normalization by Evaluation</title>
       <link>/entries/NormByEval.html</link>
       <pubDate>Mon, 18 Feb 2008 00:00:00 +0000</pubDate>
       
       <guid>/entries/NormByEval.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Quantifier Elimination for Linear Arithmetic</title>
       <link>/entries/LinearQuantifierElim.html</link>
       <pubDate>Fri, 11 Jan 2008 00:00:00 +0000</pubDate>
       
       <guid>/entries/LinearQuantifierElim.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Formalization of Conflict Analysis of Programs with Procedures, Thread Creation, and Monitors</title>
       <link>/entries/Program-Conflict-Analysis.html</link>
       <pubDate>Fri, 14 Dec 2007 00:00:00 +0000</pubDate>
       
       <guid>/entries/Program-Conflict-Analysis.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Jinja with Threads</title>
       <link>/entries/JinjaThreads.html</link>
       <pubDate>Mon, 03 Dec 2007 00:00:00 +0000</pubDate>
       
       <guid>/entries/JinjaThreads.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Much Ado About Two</title>
       <link>/entries/MuchAdoAboutTwo.html</link>
       <pubDate>Tue, 06 Nov 2007 00:00:00 +0000</pubDate>
       
       <guid>/entries/MuchAdoAboutTwo.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Fermat&#39;s Last Theorem for Exponents 3 and 4 and the Parametrisation of Pythagorean Triples</title>
       <link>/entries/Fermat3_4.html</link>
       <pubDate>Sun, 12 Aug 2007 00:00:00 +0000</pubDate>
       
       <guid>/entries/Fermat3_4.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Sums of Two and Four Squares</title>
       <link>/entries/SumSquares.html</link>
       <pubDate>Sun, 12 Aug 2007 00:00:00 +0000</pubDate>
       
       <guid>/entries/SumSquares.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Fundamental Properties of Valuation Theory and Hensel&#39;s Lemma</title>
       <link>/entries/Valuation.html</link>
       <pubDate>Wed, 08 Aug 2007 00:00:00 +0000</pubDate>
       
       <guid>/entries/Valuation.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>First-Order Logic According to Fitting</title>
       <link>/entries/FOL-Fitting.html</link>
       <pubDate>Thu, 02 Aug 2007 00:00:00 +0000</pubDate>
       
       <guid>/entries/FOL-Fitting.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>POPLmark Challenge Via de Bruijn Indices</title>
       <link>/entries/POPLmark-deBruijn.html</link>
       <pubDate>Thu, 02 Aug 2007 00:00:00 +0000</pubDate>
       
       <guid>/entries/POPLmark-deBruijn.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Hotel Key Card System</title>
       <link>/entries/HotelKeyCards.html</link>
       <pubDate>Sat, 09 Sep 2006 00:00:00 +0000</pubDate>
       
       <guid>/entries/HotelKeyCards.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Abstract Hoare Logics</title>
       <link>/entries/Abstract-Hoare-Logics.html</link>
       <pubDate>Tue, 08 Aug 2006 00:00:00 +0000</pubDate>
       
       <guid>/entries/Abstract-Hoare-Logics.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Flyspeck I: Tame Graphs</title>
       <link>/entries/Flyspeck-Tame.html</link>
       <pubDate>Mon, 22 May 2006 00:00:00 +0000</pubDate>
       
       <guid>/entries/Flyspeck-Tame.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>CoreC&#43;&#43;</title>
       <link>/entries/CoreC&#43;&#43;.html</link>
       <pubDate>Mon, 15 May 2006 00:00:00 +0000</pubDate>
       
       <guid>/entries/CoreC&#43;&#43;.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>A Theory of Featherweight Java in Isabelle/HOL</title>
       <link>/entries/FeatherweightJava.html</link>
       <pubDate>Fri, 31 Mar 2006 00:00:00 +0000</pubDate>
       
       <guid>/entries/FeatherweightJava.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Instances of Schneider&#39;s generalized protocol of clock synchronization</title>
       <link>/entries/ClockSynchInst.html</link>
       <pubDate>Wed, 15 Mar 2006 00:00:00 +0000</pubDate>
       
       <guid>/entries/ClockSynchInst.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Cauchy&#39;s Mean Theorem and the Cauchy-Schwarz Inequality</title>
       <link>/entries/Cauchy.html</link>
       <pubDate>Tue, 14 Mar 2006 00:00:00 +0000</pubDate>
       
       <guid>/entries/Cauchy.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Countable Ordinals</title>
       <link>/entries/Ordinal.html</link>
       <pubDate>Fri, 11 Nov 2005 00:00:00 +0000</pubDate>
       
       <guid>/entries/Ordinal.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Fast Fourier Transform</title>
       <link>/entries/FFT.html</link>
       <pubDate>Wed, 12 Oct 2005 00:00:00 +0000</pubDate>
       
       <guid>/entries/FFT.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Formalization of a Generalized Protocol for Clock Synchronization</title>
       <link>/entries/GenClock.html</link>
       <pubDate>Fri, 24 Jun 2005 00:00:00 +0000</pubDate>
       
       <guid>/entries/GenClock.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Proving the Correctness of Disk Paxos</title>
       <link>/entries/DiskPaxos.html</link>
       <pubDate>Wed, 22 Jun 2005 00:00:00 +0000</pubDate>
       
       <guid>/entries/DiskPaxos.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Jive Data and Store Model</title>
       <link>/entries/JiveDataStoreModel.html</link>
       <pubDate>Mon, 20 Jun 2005 00:00:00 +0000</pubDate>
       
       <guid>/entries/JiveDataStoreModel.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Jinja is not Java</title>
       <link>/entries/Jinja.html</link>
       <pubDate>Wed, 01 Jun 2005 00:00:00 +0000</pubDate>
       
       <guid>/entries/Jinja.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>SHA1, RSA, PSS and more</title>
       <link>/entries/RSAPSS.html</link>
       <pubDate>Mon, 02 May 2005 00:00:00 +0000</pubDate>
       
       <guid>/entries/RSAPSS.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Category Theory to Yoneda&#39;s Lemma</title>
       <link>/entries/Category.html</link>
       <pubDate>Thu, 21 Apr 2005 00:00:00 +0000</pubDate>
       
       <guid>/entries/Category.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>File Refinement</title>
       <link>/entries/FileRefinement.html</link>
       <pubDate>Thu, 09 Dec 2004 00:00:00 +0000</pubDate>
       
       <guid>/entries/FileRefinement.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Integration theory and random variables</title>
       <link>/entries/Integration.html</link>
       <pubDate>Fri, 19 Nov 2004 00:00:00 +0000</pubDate>
       
       <guid>/entries/Integration.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>A Mechanically Verified, Efficient, Sound and Complete Theorem Prover For First Order Logic</title>
       <link>/entries/Verified-Prover.html</link>
       <pubDate>Tue, 28 Sep 2004 00:00:00 +0000</pubDate>
       
       <guid>/entries/Verified-Prover.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Completeness theorem</title>
       <link>/entries/Completeness.html</link>
       <pubDate>Mon, 20 Sep 2004 00:00:00 +0000</pubDate>
       
       <guid>/entries/Completeness.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Ramsey&#39;s theorem, infinitary version</title>
       <link>/entries/Ramsey-Infinite.html</link>
       <pubDate>Mon, 20 Sep 2004 00:00:00 +0000</pubDate>
       
       <guid>/entries/Ramsey-Infinite.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Compiling Exceptions Correctly</title>
       <link>/entries/Compiling-Exceptions-Correctly.html</link>
       <pubDate>Fri, 09 Jul 2004 00:00:00 +0000</pubDate>
       
       <guid>/entries/Compiling-Exceptions-Correctly.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Depth First Search</title>
       <link>/entries/Depth-First-Search.html</link>
       <pubDate>Thu, 24 Jun 2004 00:00:00 +0000</pubDate>
       
       <guid>/entries/Depth-First-Search.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Groups, Rings and Modules</title>
       <link>/entries/Group-Ring-Module.html</link>
       <pubDate>Tue, 18 May 2004 00:00:00 +0000</pubDate>
       
       <guid>/entries/Group-Ring-Module.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Lazy Lists II</title>
       <link>/entries/Lazy-Lists-II.html</link>
       <pubDate>Mon, 26 Apr 2004 00:00:00 +0000</pubDate>
       
       <guid>/entries/Lazy-Lists-II.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Topology</title>
       <link>/entries/Topology.html</link>
       <pubDate>Mon, 26 Apr 2004 00:00:00 +0000</pubDate>
       
       <guid>/entries/Topology.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Binary Search Trees</title>
       <link>/entries/BinarySearchTree.html</link>
       <pubDate>Mon, 05 Apr 2004 00:00:00 +0000</pubDate>
       
       <guid>/entries/BinarySearchTree.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Functional Automata</title>
       <link>/entries/Functional-Automata.html</link>
       <pubDate>Tue, 30 Mar 2004 00:00:00 +0000</pubDate>
       
       <guid>/entries/Functional-Automata.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>AVL Trees</title>
       <link>/entries/AVL-Trees.html</link>
       <pubDate>Fri, 19 Mar 2004 00:00:00 +0000</pubDate>
       
       <guid>/entries/AVL-Trees.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Mini ML</title>
       <link>/entries/MiniML.html</link>
       <pubDate>Fri, 19 Mar 2004 00:00:00 +0000</pubDate>
       
       <guid>/entries/MiniML.html</guid>
       <description></description>
     </item>
     
     <item>
       <title>Abortable_Linearizable_Modules</title>
       <link>/theories/abortable_linearizable_modules/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/abortable_linearizable_modules/</guid>
       <description></description>
     </item>
     
     <item>
       <title>About</title>
       <link>/about/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/about/</guid>
       <description>The Archive of Formal Proofs is a collection of proof libraries, examples, and larger scientific developments, mechanically checked in the theorem prover Isabelle. It is organized in the way of a scientific journal. Submissions are refereed.
 The archive repository is hosted on Heptapod to provide easy free access to archive entries. The entries are tested and maintained continuously against the current stable release of Isabelle. Older versions of archive entries will remain available.</description>
     </item>
     
     <item>
       <title>Abs_Int_ITP2012</title>
       <link>/theories/abs_int_itp2012/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/abs_int_itp2012/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Abstract-Hoare-Logics</title>
       <link>/theories/abstract-hoare-logics/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/abstract-hoare-logics/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Abstract-Rewriting</title>
       <link>/theories/abstract-rewriting/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/abstract-rewriting/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Abstract_Completeness</title>
       <link>/theories/abstract_completeness/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/abstract_completeness/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Abstract_Soundness</title>
       <link>/theories/abstract_soundness/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/abstract_soundness/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Ackermanns_not_PR</title>
       <link>/theories/ackermanns_not_pr/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/ackermanns_not_pr/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Actuarial_Mathematics</title>
       <link>/theories/actuarial_mathematics/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/actuarial_mathematics/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Adaptive_State_Counting</title>
       <link>/theories/adaptive_state_counting/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/adaptive_state_counting/</guid>
       <description></description>
     </item>
     
     <item>
       <title>ADS_Functor</title>
       <link>/theories/ads_functor/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/ads_functor/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Affine_Arithmetic</title>
       <link>/theories/affine_arithmetic/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/affine_arithmetic/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Aggregation_Algebras</title>
       <link>/theories/aggregation_algebras/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/aggregation_algebras/</guid>
       <description></description>
     </item>
     
     <item>
       <title>AI_Planning_Languages_Semantics</title>
       <link>/theories/ai_planning_languages_semantics/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/ai_planning_languages_semantics/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Akra_Bazzi</title>
       <link>/theories/akra_bazzi/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/akra_bazzi/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Algebraic_Numbers</title>
       <link>/theories/algebraic_numbers/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/algebraic_numbers/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Algebraic_VCs</title>
       <link>/theories/algebraic_vcs/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/algebraic_vcs/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Allen_Calculus</title>
       <link>/theories/allen_calculus/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/allen_calculus/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Amicable_Numbers</title>
       <link>/theories/amicable_numbers/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/amicable_numbers/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Amortized_Complexity</title>
       <link>/theories/amortized_complexity/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/amortized_complexity/</guid>
       <description></description>
     </item>
     
     <item>
       <title>AnselmGod</title>
       <link>/theories/anselmgod/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/anselmgod/</guid>
       <description></description>
     </item>
     
     <item>
       <title>AODV</title>
       <link>/theories/aodv/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/aodv/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Applicative_Lifting</title>
       <link>/theories/applicative_lifting/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/applicative_lifting/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Approximation_Algorithms</title>
       <link>/theories/approximation_algorithms/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/approximation_algorithms/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Architectural_Design_Patterns</title>
       <link>/theories/architectural_design_patterns/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/architectural_design_patterns/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Aristotles_Assertoric_Syllogistic</title>
       <link>/theories/aristotles_assertoric_syllogistic/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/aristotles_assertoric_syllogistic/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Arith_Prog_Rel_Primes</title>
       <link>/theories/arith_prog_rel_primes/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/arith_prog_rel_primes/</guid>
       <description></description>
     </item>
     
     <item>
       <title>ArrowImpossibilityGS</title>
       <link>/theories/arrowimpossibilitygs/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/arrowimpossibilitygs/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Attack_Trees</title>
       <link>/theories/attack_trees/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/attack_trees/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Auto2_HOL</title>
       <link>/theories/auto2_hol/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/auto2_hol/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Auto2_Imperative_HOL</title>
       <link>/theories/auto2_imperative_hol/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/auto2_imperative_hol/</guid>
       <description></description>
     </item>
     
     <item>
       <title>AutoFocus-Stream</title>
       <link>/theories/autofocus-stream/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/autofocus-stream/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Automated_Stateful_Protocol_Verification</title>
       <link>/theories/automated_stateful_protocol_verification/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/automated_stateful_protocol_verification/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Automatic_Refinement</title>
       <link>/theories/automatic_refinement/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/automatic_refinement/</guid>
       <description></description>
     </item>
     
     <item>
       <title>AVL-Trees</title>
       <link>/theories/avl-trees/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/avl-trees/</guid>
       <description></description>
     </item>
     
     <item>
       <title>AWN</title>
       <link>/theories/awn/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/awn/</guid>
       <description></description>
     </item>
     
     <item>
       <title>AxiomaticCategoryTheory</title>
       <link>/theories/axiomaticcategorytheory/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/axiomaticcategorytheory/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Balog_Szemeredi_Gowers</title>
       <link>/theories/balog_szemeredi_gowers/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/balog_szemeredi_gowers/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Banach_Steinhaus</title>
       <link>/theories/banach_steinhaus/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/banach_steinhaus/</guid>
       <description></description>
     </item>
     
     <item>
       <title>BD_Security_Compositional</title>
       <link>/theories/bd_security_compositional/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/bd_security_compositional/</guid>
       <description></description>
     </item>
     
     <item>
       <title>BDD</title>
       <link>/theories/bdd/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/bdd/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Belief_Revision</title>
       <link>/theories/belief_revision/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/belief_revision/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Bell_Numbers_Spivey</title>
       <link>/theories/bell_numbers_spivey/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/bell_numbers_spivey/</guid>
       <description></description>
     </item>
     
     <item>
       <title>BenOr_Kozen_Reif</title>
       <link>/theories/benor_kozen_reif/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/benor_kozen_reif/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Berlekamp_Zassenhaus</title>
       <link>/theories/berlekamp_zassenhaus/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/berlekamp_zassenhaus/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Bernoulli</title>
       <link>/theories/bernoulli/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/bernoulli/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Bertrands_Postulate</title>
       <link>/theories/bertrands_postulate/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/bertrands_postulate/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Bicategory</title>
       <link>/theories/bicategory/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/bicategory/</guid>
       <description></description>
     </item>
     
     <item>
       <title>BinarySearchTree</title>
       <link>/theories/binarysearchtree/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/binarysearchtree/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Binding_Syntax_Theory</title>
       <link>/theories/binding_syntax_theory/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/binding_syntax_theory/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Binomial-Heaps</title>
       <link>/theories/binomial-heaps/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/binomial-heaps/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Binomial-Queues</title>
       <link>/theories/binomial-queues/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/binomial-queues/</guid>
       <description></description>
     </item>
     
     <item>
       <title>BirdKMP</title>
       <link>/theories/birdkmp/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/birdkmp/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Blue_Eyes</title>
       <link>/theories/blue_eyes/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/blue_eyes/</guid>
       <description></description>
     </item>
     
     <item>
       <title>BNF_CC</title>
       <link>/theories/bnf_cc/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/bnf_cc/</guid>
       <description></description>
     </item>
     
     <item>
       <title>BNF_Operations</title>
       <link>/theories/bnf_operations/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/bnf_operations/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Bondy</title>
       <link>/theories/bondy/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/bondy/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Boolean_Expression_Checkers</title>
       <link>/theories/boolean_expression_checkers/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/boolean_expression_checkers/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Boolos_Curious_Inference</title>
       <link>/theories/boolos_curious_inference/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/boolos_curious_inference/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Bounded_Deducibility_Security</title>
       <link>/theories/bounded_deducibility_security/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/bounded_deducibility_security/</guid>
       <description></description>
     </item>
     
     <item>
       <title>BTree</title>
       <link>/theories/btree/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/btree/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Buchi_Complementation</title>
       <link>/theories/buchi_complementation/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/buchi_complementation/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Budan_Fourier</title>
       <link>/theories/budan_fourier/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/budan_fourier/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Buffons_Needle</title>
       <link>/theories/buffons_needle/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/buffons_needle/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Buildings</title>
       <link>/theories/buildings/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/buildings/</guid>
       <description></description>
     </item>
     
     <item>
       <title>BytecodeLogicJmlTypes</title>
       <link>/theories/bytecodelogicjmltypes/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/bytecodelogicjmltypes/</guid>
       <description></description>
     </item>
     
     <item>
       <title>C2KA_DistributedSystems</title>
       <link>/theories/c2ka_distributedsystems/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/c2ka_distributedsystems/</guid>
       <description></description>
     </item>
     
     <item>
       <title>CakeML</title>
       <link>/theories/cakeml/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/cakeml/</guid>
       <description></description>
     </item>
     
     <item>
       <title>CakeML_Codegen</title>
       <link>/theories/cakeml_codegen/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/cakeml_codegen/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Call_Arity</title>
       <link>/theories/call_arity/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/call_arity/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Card_Equiv_Relations</title>
       <link>/theories/card_equiv_relations/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/card_equiv_relations/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Card_Multisets</title>
       <link>/theories/card_multisets/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/card_multisets/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Card_Number_Partitions</title>
       <link>/theories/card_number_partitions/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/card_number_partitions/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Card_Partitions</title>
       <link>/theories/card_partitions/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/card_partitions/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Cartan_FP</title>
       <link>/theories/cartan_fp/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/cartan_fp/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Case_Labeling</title>
       <link>/theories/case_labeling/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/case_labeling/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Catalan_Numbers</title>
       <link>/theories/catalan_numbers/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/catalan_numbers/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Category</title>
       <link>/theories/category/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/category/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Category2</title>
       <link>/theories/category2/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/category2/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Category3</title>
       <link>/theories/category3/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/category3/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Cauchy</title>
       <link>/theories/cauchy/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/cauchy/</guid>
       <description></description>
     </item>
     
     <item>
       <title>CAVA_Automata</title>
       <link>/theories/cava_automata/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/cava_automata/</guid>
       <description></description>
     </item>
     
     <item>
       <title>CAVA_Base</title>
       <link>/theories/cava_base/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/cava_base/</guid>
       <description></description>
     </item>
     
     <item>
       <title>CAVA_LTL_Modelchecker</title>
       <link>/theories/cava_ltl_modelchecker/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/cava_ltl_modelchecker/</guid>
       <description></description>
     </item>
     
     <item>
       <title>CAVA_Setup</title>
       <link>/theories/cava_setup/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/cava_setup/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Cayley_Hamilton</title>
       <link>/theories/cayley_hamilton/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/cayley_hamilton/</guid>
       <description></description>
     </item>
     
     <item>
       <title>CCS</title>
       <link>/theories/ccs/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/ccs/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Certification_Monads</title>
       <link>/theories/certification_monads/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/certification_monads/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Chandy_Lamport</title>
       <link>/theories/chandy_lamport/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/chandy_lamport/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Chord_Segments</title>
       <link>/theories/chord_segments/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/chord_segments/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Circus</title>
       <link>/theories/circus/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/circus/</guid>
       <description></description>
     </item>
     
     <item>
       <title>CISC-Kernel</title>
       <link>/theories/cisc-kernel/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/cisc-kernel/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Clean</title>
       <link>/theories/clean/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/clean/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Clique_and_Monotone_Circuits</title>
       <link>/theories/clique_and_monotone_circuits/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/clique_and_monotone_circuits/</guid>
       <description></description>
     </item>
     
     <item>
       <title>ClockSynchInst</title>
       <link>/theories/clocksynchinst/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/clocksynchinst/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Closest_Pair_Points</title>
       <link>/theories/closest_pair_points/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/closest_pair_points/</guid>
       <description></description>
     </item>
     
     <item>
       <title>CoCon</title>
       <link>/theories/cocon/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/cocon/</guid>
       <description></description>
     </item>
     
     <item>
       <title>CofGroups</title>
       <link>/theories/cofgroups/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/cofgroups/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Coinductive</title>
       <link>/theories/coinductive/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/coinductive/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Coinductive_Languages</title>
       <link>/theories/coinductive_languages/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/coinductive_languages/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Collections</title>
       <link>/theories/collections/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/collections/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Collections_Examples</title>
       <link>/theories/collections_examples/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/collections_examples/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Combinable_Wands</title>
       <link>/theories/combinable_wands/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/combinable_wands/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Combinatorial_Enumeration_Algorithms</title>
       <link>/theories/combinatorial_enumeration_algorithms/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/combinatorial_enumeration_algorithms/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Combinatorics_Words</title>
       <link>/theories/combinatorics_words/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/combinatorics_words/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Combinatorics_Words_Graph_Lemma</title>
       <link>/theories/combinatorics_words_graph_lemma/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/combinatorics_words_graph_lemma/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Combinatorics_Words_Lyndon</title>
       <link>/theories/combinatorics_words_lyndon/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/combinatorics_words_lyndon/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Commuting_Hermitian</title>
       <link>/theories/commuting_hermitian/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/commuting_hermitian/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Comparison_Sort_Lower_Bound</title>
       <link>/theories/comparison_sort_lower_bound/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/comparison_sort_lower_bound/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Compiling-Exceptions-Correctly</title>
       <link>/theories/compiling-exceptions-correctly/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/compiling-exceptions-correctly/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Complete_Non_Orders</title>
       <link>/theories/complete_non_orders/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/complete_non_orders/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Completeness</title>
       <link>/theories/completeness/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/completeness/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Complex_Bounded_Operators</title>
       <link>/theories/complex_bounded_operators/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/complex_bounded_operators/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Complex_Geometry</title>
       <link>/theories/complex_geometry/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/complex_geometry/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Complx</title>
       <link>/theories/complx/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/complx/</guid>
       <description></description>
     </item>
     
     <item>
       <title>ComponentDependencies</title>
       <link>/theories/componentdependencies/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/componentdependencies/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Concurrent_Ref_Alg</title>
       <link>/theories/concurrent_ref_alg/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/concurrent_ref_alg/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Concurrent_Revisions</title>
       <link>/theories/concurrent_revisions/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/concurrent_revisions/</guid>
       <description></description>
     </item>
     
     <item>
       <title>ConcurrentGC</title>
       <link>/theories/concurrentgc/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/concurrentgc/</guid>
       <description></description>
     </item>
     
     <item>
       <title>ConcurrentIMP</title>
       <link>/theories/concurrentimp/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/concurrentimp/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Conditional_Simplification</title>
       <link>/theories/conditional_simplification/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/conditional_simplification/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Conditional_Transfer_Rule</title>
       <link>/theories/conditional_transfer_rule/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/conditional_transfer_rule/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Consensus_Refined</title>
       <link>/theories/consensus_refined/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/consensus_refined/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Constructive_Cryptography</title>
       <link>/theories/constructive_cryptography/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/constructive_cryptography/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Constructive_Cryptography_CM</title>
       <link>/theories/constructive_cryptography_cm/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/constructive_cryptography_cm/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Constructor_Funs</title>
       <link>/theories/constructor_funs/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/constructor_funs/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Containers</title>
       <link>/theories/containers/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/containers/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Containers-Benchmarks</title>
       <link>/theories/containers-benchmarks/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/containers-benchmarks/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Core_DOM</title>
       <link>/theories/core_dom/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/core_dom/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Core_SC_DOM</title>
       <link>/theories/core_sc_dom/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/core_sc_dom/</guid>
       <description></description>
     </item>
     
     <item>
       <title>CoreC&#43;&#43;</title>
       <link>/theories/corec&#43;&#43;/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/corec&#43;&#43;/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Correctness_Algebras</title>
       <link>/theories/correctness_algebras/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/correctness_algebras/</guid>
       <description></description>
     </item>
     
     <item>
       <title>CoSMed</title>
       <link>/theories/cosmed/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/cosmed/</guid>
       <description></description>
     </item>
     
     <item>
       <title>CoSMeDis</title>
       <link>/theories/cosmedis/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/cosmedis/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Cotangent_PFD_Formula</title>
       <link>/theories/cotangent_pfd_formula/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/cotangent_pfd_formula/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Count_Complex_Roots</title>
       <link>/theories/count_complex_roots/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/count_complex_roots/</guid>
       <description></description>
     </item>
     
     <item>
       <title>CRDT</title>
       <link>/theories/crdt/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/crdt/</guid>
       <description></description>
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     <item>
       <title>CryptHOL</title>
       <link>/theories/crypthol/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/crypthol/</guid>
       <description></description>
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     <item>
       <title>CryptoBasedCompositionalProperties</title>
       <link>/theories/cryptobasedcompositionalproperties/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/cryptobasedcompositionalproperties/</guid>
       <description></description>
     </item>
     
     <item>
       <title>CRYSTALS-Kyber</title>
       <link>/theories/crystals-kyber/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/crystals-kyber/</guid>
       <description></description>
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     <item>
       <title>CSP_RefTK</title>
       <link>/theories/csp_reftk/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/csp_reftk/</guid>
       <description></description>
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     <item>
       <title>Cubic_Quartic_Equations</title>
       <link>/theories/cubic_quartic_equations/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/cubic_quartic_equations/</guid>
       <description></description>
     </item>
     
     <item>
       <title>CYK</title>
       <link>/theories/cyk/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/cyk/</guid>
       <description></description>
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     <item>
       <title>CZH_Elementary_Categories</title>
       <link>/theories/czh_elementary_categories/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/czh_elementary_categories/</guid>
       <description></description>
     </item>
     
     <item>
       <title>CZH_Foundations</title>
       <link>/theories/czh_foundations/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/czh_foundations/</guid>
       <description></description>
     </item>
     
     <item>
       <title>CZH_Universal_Constructions</title>
       <link>/theories/czh_universal_constructions/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/czh_universal_constructions/</guid>
       <description></description>
     </item>
     
     <item>
       <title>DataRefinementIBP</title>
       <link>/theories/datarefinementibp/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/datarefinementibp/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Datatype_Order_Generator</title>
       <link>/theories/datatype_order_generator/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/datatype_order_generator/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Decl_Sem_Fun_PL</title>
       <link>/theories/decl_sem_fun_pl/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/decl_sem_fun_pl/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Decreasing-Diagrams</title>
       <link>/theories/decreasing-diagrams/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/decreasing-diagrams/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Decreasing-Diagrams-II</title>
       <link>/theories/decreasing-diagrams-ii/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/decreasing-diagrams-ii/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Dedekind_Real</title>
       <link>/theories/dedekind_real/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/dedekind_real/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Deep_Learning</title>
       <link>/theories/deep_learning/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/deep_learning/</guid>
       <description></description>
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     <item>
       <title>Delta_System_Lemma</title>
       <link>/theories/delta_system_lemma/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/delta_system_lemma/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Density_Compiler</title>
       <link>/theories/density_compiler/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/density_compiler/</guid>
       <description></description>
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     <item>
       <title>Dependent_SIFUM_Refinement</title>
       <link>/theories/dependent_sifum_refinement/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/dependent_sifum_refinement/</guid>
       <description></description>
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     <item>
       <title>Dependent_SIFUM_Type_Systems</title>
       <link>/theories/dependent_sifum_type_systems/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/dependent_sifum_type_systems/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Depth-First-Search</title>
       <link>/theories/depth-first-search/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/depth-first-search/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Derangements</title>
       <link>/theories/derangements/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/derangements/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Deriving</title>
       <link>/theories/deriving/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/deriving/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Descartes_Sign_Rule</title>
       <link>/theories/descartes_sign_rule/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/descartes_sign_rule/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Design_Theory</title>
       <link>/theories/design_theory/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/design_theory/</guid>
       <description></description>
     </item>
     
     <item>
       <title>DFS_Framework</title>
       <link>/theories/dfs_framework/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/dfs_framework/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Dict_Construction</title>
       <link>/theories/dict_construction/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/dict_construction/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Differential_Dynamic_Logic</title>
       <link>/theories/differential_dynamic_logic/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/differential_dynamic_logic/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Differential_Game_Logic</title>
       <link>/theories/differential_game_logic/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/differential_game_logic/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Digit_Expansions</title>
       <link>/theories/digit_expansions/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/digit_expansions/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Dijkstra_Shortest_Path</title>
       <link>/theories/dijkstra_shortest_path/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/dijkstra_shortest_path/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Diophantine_Eqns_Lin_Hom</title>
       <link>/theories/diophantine_eqns_lin_hom/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/diophantine_eqns_lin_hom/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Dirichlet_L</title>
       <link>/theories/dirichlet_l/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/dirichlet_l/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Dirichlet_Series</title>
       <link>/theories/dirichlet_series/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/dirichlet_series/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Discrete_Summation</title>
       <link>/theories/discrete_summation/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/discrete_summation/</guid>
       <description></description>
     </item>
     
     <item>
       <title>DiscretePricing</title>
       <link>/theories/discretepricing/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/discretepricing/</guid>
       <description></description>
     </item>
     
     <item>
       <title>DiskPaxos</title>
       <link>/theories/diskpaxos/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/diskpaxos/</guid>
       <description></description>
     </item>
     
     <item>
       <title>DOM_Components</title>
       <link>/theories/dom_components/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/dom_components/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Dominance_CHK</title>
       <link>/theories/dominance_chk/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/dominance_chk/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Download the Archive</title>
       <link>/download/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/download/</guid>
       <description>Current stable version (for most recent Isabelle release): Download all sessions: afp-current.tar.gz (~70 MB)
 Older stable versions: Please use the sourceforge download system to access older versions of the archive.
 Mercurial access: The AFP repositories with tooling and metadata can be found at Heptapod. In particular, the development version of the Archive (for the development version of Isabelle) is available there.
 How to refer to AFP entries: You can refer to AFP entries by using the AFP as an Isabelle component.</description>
     </item>
     
     <item>
       <title>DPRM_Theorem</title>
       <link>/theories/dprm_theorem/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/dprm_theorem/</guid>
       <description></description>
     </item>
     
     <item>
       <title>DPT-SAT-Solver</title>
       <link>/theories/dpt-sat-solver/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/dpt-sat-solver/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Dynamic_Tables</title>
       <link>/theories/dynamic_tables/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/dynamic_tables/</guid>
       <description></description>
     </item>
     
     <item>
       <title>DynamicArchitectures</title>
       <link>/theories/dynamicarchitectures/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/dynamicarchitectures/</guid>
       <description></description>
     </item>
     
     <item>
       <title>E_Transcendental</title>
       <link>/theories/e_transcendental/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/e_transcendental/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Echelon_Form</title>
       <link>/theories/echelon_form/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/echelon_form/</guid>
       <description></description>
     </item>
     
     <item>
       <title>EdmondsKarp_Maxflow</title>
       <link>/theories/edmondskarp_maxflow/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/edmondskarp_maxflow/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Efficient-Mergesort</title>
       <link>/theories/efficient-mergesort/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/efficient-mergesort/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Elliptic_Curves_Group_Law</title>
       <link>/theories/elliptic_curves_group_law/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/elliptic_curves_group_law/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Encodability_Process_Calculi</title>
       <link>/theories/encodability_process_calculi/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/encodability_process_calculi/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Entry Submission</title>
       <link>/submission/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/submission/</guid>
       <description>Submission Guidelines The submission must follow the following Isabelle style rules. For additional guidelines on Isabelle proofs, also see the this guide (feel free to follow all of these; only the below are mandatory). Technical details about the submission process and the format of the submission are explained on the submission site.
  No use of the commands sorry or back. Instantiations must not use Isabelle-generated names such as xa — use Isar, the subgoal command or rename_tac to avoid such names.</description>
     </item>
     
     <item>
       <title>Epistemic_Logic</title>
       <link>/theories/epistemic_logic/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/epistemic_logic/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Equivalence_Relation_Enumeration</title>
       <link>/theories/equivalence_relation_enumeration/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/equivalence_relation_enumeration/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Ergodic_Theory</title>
       <link>/theories/ergodic_theory/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/ergodic_theory/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Error_Function</title>
       <link>/theories/error_function/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/error_function/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Euler_MacLaurin</title>
       <link>/theories/euler_maclaurin/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/euler_maclaurin/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Euler_Partition</title>
       <link>/theories/euler_partition/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/euler_partition/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Eval_FO</title>
       <link>/theories/eval_fo/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/eval_fo/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Extended_Finite_State_Machine_Inference</title>
       <link>/theories/extended_finite_state_machine_inference/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/extended_finite_state_machine_inference/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Extended_Finite_State_Machines</title>
       <link>/theories/extended_finite_state_machines/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/extended_finite_state_machines/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Factor_Algebraic_Polynomial</title>
       <link>/theories/factor_algebraic_polynomial/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/factor_algebraic_polynomial/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Factored_Transition_System_Bounding</title>
       <link>/theories/factored_transition_system_bounding/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/factored_transition_system_bounding/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Falling_Factorial_Sum</title>
       <link>/theories/falling_factorial_sum/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/falling_factorial_sum/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Farkas</title>
       <link>/theories/farkas/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/farkas/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Featherweight_OCL</title>
       <link>/theories/featherweight_ocl/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/featherweight_ocl/</guid>
       <description></description>
     </item>
     
     <item>
       <title>FeatherweightJava</title>
       <link>/theories/featherweightjava/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/featherweightjava/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Fermat3_4</title>
       <link>/theories/fermat3_4/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/fermat3_4/</guid>
       <description></description>
     </item>
     
     <item>
       <title>FFT</title>
       <link>/theories/fft/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/fft/</guid>
       <description></description>
     </item>
     
     <item>
       <title>FileRefinement</title>
       <link>/theories/filerefinement/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/filerefinement/</guid>
       <description></description>
     </item>
     
     <item>
       <title>FinFun</title>
       <link>/theories/finfun/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/finfun/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Finger-Trees</title>
       <link>/theories/finger-trees/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/finger-trees/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Finite-Map-Extras</title>
       <link>/theories/finite-map-extras/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/finite-map-extras/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Finite_Automata_HF</title>
       <link>/theories/finite_automata_hf/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/finite_automata_hf/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Finite_Fields</title>
       <link>/theories/finite_fields/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/finite_fields/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Finitely_Generated_Abelian_Groups</title>
       <link>/theories/finitely_generated_abelian_groups/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/finitely_generated_abelian_groups/</guid>
       <description></description>
     </item>
     
     <item>
       <title>First_Order_Terms</title>
       <link>/theories/first_order_terms/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/first_order_terms/</guid>
       <description></description>
     </item>
     
     <item>
       <title>First_Welfare_Theorem</title>
       <link>/theories/first_welfare_theorem/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/first_welfare_theorem/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Fishburn_Impossibility</title>
       <link>/theories/fishburn_impossibility/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/fishburn_impossibility/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Fisher_Yates</title>
       <link>/theories/fisher_yates/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/fisher_yates/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Fishers_Inequality</title>
       <link>/theories/fishers_inequality/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/fishers_inequality/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Flow_Networks</title>
       <link>/theories/flow_networks/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/flow_networks/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Floyd_Warshall</title>
       <link>/theories/floyd_warshall/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/floyd_warshall/</guid>
       <description></description>
     </item>
     
     <item>
       <title>FLP</title>
       <link>/theories/flp/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/flp/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Flyspeck-Tame</title>
       <link>/theories/flyspeck-tame/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/flyspeck-tame/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Flyspeck-Tame-Computation</title>
       <link>/theories/flyspeck-tame-computation/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/flyspeck-tame-computation/</guid>
       <description></description>
     </item>
     
     <item>
       <title>FO_Theory_Rewriting</title>
       <link>/theories/fo_theory_rewriting/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/fo_theory_rewriting/</guid>
       <description></description>
     </item>
     
     <item>
       <title>FocusStreamsCaseStudies</title>
       <link>/theories/focusstreamscasestudies/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/focusstreamscasestudies/</guid>
       <description></description>
     </item>
     
     <item>
       <title>FOL-Fitting</title>
       <link>/theories/fol-fitting/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/fol-fitting/</guid>
       <description></description>
     </item>
     
     <item>
       <title>FOL_Axiomatic</title>
       <link>/theories/fol_axiomatic/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/fol_axiomatic/</guid>
       <description></description>
     </item>
     
     <item>
       <title>FOL_Harrison</title>
       <link>/theories/fol_harrison/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/fol_harrison/</guid>
       <description></description>
     </item>
     
     <item>
       <title>FOL_Seq_Calc1</title>
       <link>/theories/fol_seq_calc1/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/fol_seq_calc1/</guid>
       <description></description>
     </item>
     
     <item>
       <title>FOL_Seq_Calc2</title>
       <link>/theories/fol_seq_calc2/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/fol_seq_calc2/</guid>
       <description></description>
     </item>
     
     <item>
       <title>FOL_Seq_Calc3</title>
       <link>/theories/fol_seq_calc3/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/fol_seq_calc3/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Forcing</title>
       <link>/theories/forcing/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/forcing/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Formal_Puiseux_Series</title>
       <link>/theories/formal_puiseux_series/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/formal_puiseux_series/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Formal_SSA</title>
       <link>/theories/formal_ssa/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/formal_ssa/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Formula_Derivatives</title>
       <link>/theories/formula_derivatives/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/formula_derivatives/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Formula_Derivatives-Examples</title>
       <link>/theories/formula_derivatives-examples/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/formula_derivatives-examples/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Foundation_of_geometry</title>
       <link>/theories/foundation_of_geometry/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/foundation_of_geometry/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Fourier</title>
       <link>/theories/fourier/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/fourier/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Free-Boolean-Algebra</title>
       <link>/theories/free-boolean-algebra/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/free-boolean-algebra/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Free-Groups</title>
       <link>/theories/free-groups/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/free-groups/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Frequency_Moments</title>
       <link>/theories/frequency_moments/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/frequency_moments/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Fresh_Identifiers</title>
       <link>/theories/fresh_identifiers/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/fresh_identifiers/</guid>
       <description></description>
     </item>
     
     <item>
       <title>FSM_Tests</title>
       <link>/theories/fsm_tests/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/fsm_tests/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Functional-Automata</title>
       <link>/theories/functional-automata/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/functional-automata/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Functional_Ordered_Resolution_Prover</title>
       <link>/theories/functional_ordered_resolution_prover/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/functional_ordered_resolution_prover/</guid>
       <description></description>
     </item>
     
     <item>
       <title>FunWithFunctions</title>
       <link>/theories/funwithfunctions/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/funwithfunctions/</guid>
       <description></description>
     </item>
     
     <item>
       <title>FunWithTilings</title>
       <link>/theories/funwithtilings/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/funwithtilings/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Furstenberg_Topology</title>
       <link>/theories/furstenberg_topology/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/furstenberg_topology/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Gabow_SCC</title>
       <link>/theories/gabow_scc/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/gabow_scc/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Gale_Shapley</title>
       <link>/theories/gale_shapley/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/gale_shapley/</guid>
       <description></description>
     </item>
     
     <item>
       <title>GaleStewart_Games</title>
       <link>/theories/galestewart_games/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/galestewart_games/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Game_Based_Crypto</title>
       <link>/theories/game_based_crypto/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/game_based_crypto/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Gauss-Jordan-Elim-Fun</title>
       <link>/theories/gauss-jordan-elim-fun/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/gauss-jordan-elim-fun/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Gauss_Jordan</title>
       <link>/theories/gauss_jordan/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/gauss_jordan/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Gauss_Sums</title>
       <link>/theories/gauss_sums/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/gauss_sums/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Gaussian_Integers</title>
       <link>/theories/gaussian_integers/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/gaussian_integers/</guid>
       <description></description>
     </item>
     
     <item>
       <title>GenClock</title>
       <link>/theories/genclock/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/genclock/</guid>
       <description></description>
     </item>
     
     <item>
       <title>General-Triangle</title>
       <link>/theories/general-triangle/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/general-triangle/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Generalized_Counting_Sort</title>
       <link>/theories/generalized_counting_sort/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/generalized_counting_sort/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Generic_Deriving</title>
       <link>/theories/generic_deriving/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/generic_deriving/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Generic_Join</title>
       <link>/theories/generic_join/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/generic_join/</guid>
       <description></description>
     </item>
     
     <item>
       <title>GewirthPGCProof</title>
       <link>/theories/gewirthpgcproof/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/gewirthpgcproof/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Girth_Chromatic</title>
       <link>/theories/girth_chromatic/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/girth_chromatic/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Goedel_HFSet_Semantic</title>
       <link>/theories/goedel_hfset_semantic/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/goedel_hfset_semantic/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Goedel_HFSet_Semanticless</title>
       <link>/theories/goedel_hfset_semanticless/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/goedel_hfset_semanticless/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Goedel_Incompleteness</title>
       <link>/theories/goedel_incompleteness/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/goedel_incompleteness/</guid>
       <description></description>
     </item>
     
     <item>
       <title>GoedelGod</title>
       <link>/theories/goedelgod/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/goedelgod/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Goodstein_Lambda</title>
       <link>/theories/goodstein_lambda/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/goodstein_lambda/</guid>
       <description></description>
     </item>
     
     <item>
       <title>GPU_Kernel_PL</title>
       <link>/theories/gpu_kernel_pl/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/gpu_kernel_pl/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Graph_Saturation</title>
       <link>/theories/graph_saturation/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/graph_saturation/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Graph_Theory</title>
       <link>/theories/graph_theory/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/graph_theory/</guid>
       <description></description>
     </item>
     
     <item>
       <title>GraphMarkingIBP</title>
       <link>/theories/graphmarkingibp/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/graphmarkingibp/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Green</title>
       <link>/theories/green/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/green/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Groebner_Bases</title>
       <link>/theories/groebner_bases/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/groebner_bases/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Groebner_Macaulay</title>
       <link>/theories/groebner_macaulay/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/groebner_macaulay/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Gromov_Hyperbolicity</title>
       <link>/theories/gromov_hyperbolicity/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/gromov_hyperbolicity/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Grothendieck_Schemes</title>
       <link>/theories/grothendieck_schemes/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/grothendieck_schemes/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Group-Ring-Module</title>
       <link>/theories/group-ring-module/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/group-ring-module/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Hahn_Jordan_Decomposition</title>
       <link>/theories/hahn_jordan_decomposition/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/hahn_jordan_decomposition/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Hales_Jewett</title>
       <link>/theories/hales_jewett/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/hales_jewett/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Heard_Of</title>
       <link>/theories/heard_of/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/heard_of/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Hello_World</title>
       <link>/theories/hello_world/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/hello_world/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Help</title>
       <link>/help/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/help/</guid>
       <description>This section focuses on the Archive of Formal Proofs. For help with Isabelle, see the Isabelle Documentation. More resources are listed in the Isabelle Quick Access Links.
 Referring to AFP Entries in Isabelle/JEdit Once you have downloaded the AFP, you can include its articles and theories in your own developments. If you would like to make your work available to others without having to include the AFP articles you depend on, here is how to do it.</description>
     </item>
     
     <item>
       <title>HereditarilyFinite</title>
       <link>/theories/hereditarilyfinite/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/hereditarilyfinite/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Hermite</title>
       <link>/theories/hermite/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/hermite/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Hermite_Lindemann</title>
       <link>/theories/hermite_lindemann/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/hermite_lindemann/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Hidden_Markov_Models</title>
       <link>/theories/hidden_markov_models/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/hidden_markov_models/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Higher_Order_Terms</title>
       <link>/theories/higher_order_terms/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/higher_order_terms/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Hoare_Time</title>
       <link>/theories/hoare_time/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/hoare_time/</guid>
       <description></description>
     </item>
     
     <item>
       <title>HOL-CSP</title>
       <link>/theories/hol-csp/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/hol-csp/</guid>
       <description></description>
     </item>
     
     <item>
       <title>HOL-ODE-ARCH-COMP</title>
       <link>/theories/hol-ode-arch-comp/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/hol-ode-arch-comp/</guid>
       <description></description>
     </item>
     
     <item>
       <title>HOL-ODE-Examples</title>
       <link>/theories/hol-ode-examples/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/hol-ode-examples/</guid>
       <description></description>
     </item>
     
     <item>
       <title>HOL-ODE-Numerics</title>
       <link>/theories/hol-ode-numerics/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/hol-ode-numerics/</guid>
       <description></description>
     </item>
     
     <item>
       <title>HOLCF-Prelude</title>
       <link>/theories/holcf-prelude/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/holcf-prelude/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Hood_Melville_Queue</title>
       <link>/theories/hood_melville_queue/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/hood_melville_queue/</guid>
       <description></description>
     </item>
     
     <item>
       <title>HotelKeyCards</title>
       <link>/theories/hotelkeycards/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/hotelkeycards/</guid>
       <description></description>
     </item>
     
     <item>
       <title>HRB-Slicing</title>
       <link>/theories/hrb-slicing/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/hrb-slicing/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Huffman</title>
       <link>/theories/huffman/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/huffman/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Hybrid_Logic</title>
       <link>/theories/hybrid_logic/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/hybrid_logic/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Hybrid_Multi_Lane_Spatial_Logic</title>
       <link>/theories/hybrid_multi_lane_spatial_logic/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/hybrid_multi_lane_spatial_logic/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Hybrid_Systems_VCs</title>
       <link>/theories/hybrid_systems_vcs/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/hybrid_systems_vcs/</guid>
       <description></description>
     </item>
     
     <item>
       <title>HyperCTL</title>
       <link>/theories/hyperctl/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/hyperctl/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Hyperdual</title>
       <link>/theories/hyperdual/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/hyperdual/</guid>
       <description></description>
     </item>
     
     <item>
       <title>IEEE_Floating_Point</title>
       <link>/theories/ieee_floating_point/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/ieee_floating_point/</guid>
       <description></description>
     </item>
     
     <item>
       <title>IFC_Tracking</title>
       <link>/theories/ifc_tracking/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/ifc_tracking/</guid>
       <description></description>
     </item>
     
     <item>
       <title>IMAP-CRDT</title>
       <link>/theories/imap-crdt/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/imap-crdt/</guid>
       <description></description>
     </item>
     
     <item>
       <title>IMO2019</title>
       <link>/theories/imo2019/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/imo2019/</guid>
       <description></description>
     </item>
     
     <item>
       <title>IMP2</title>
       <link>/theories/imp2/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/imp2/</guid>
       <description></description>
     </item>
     
     <item>
       <title>IMP2_Binary_Heap</title>
       <link>/theories/imp2_binary_heap/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/imp2_binary_heap/</guid>
       <description></description>
     </item>
     
     <item>
       <title>IMP_Compiler</title>
       <link>/theories/imp_compiler/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/imp_compiler/</guid>
       <description></description>
     </item>
     
     <item>
       <title>IMP_Compiler_Reuse</title>
       <link>/theories/imp_compiler_reuse/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/imp_compiler_reuse/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Imperative_Insertion_Sort</title>
       <link>/theories/imperative_insertion_sort/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/imperative_insertion_sort/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Implicational_Logic</title>
       <link>/theories/implicational_logic/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/implicational_logic/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Impossible_Geometry</title>
       <link>/theories/impossible_geometry/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/impossible_geometry/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Incompleteness</title>
       <link>/theories/incompleteness/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/incompleteness/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Incredible_Proof_Machine</title>
       <link>/theories/incredible_proof_machine/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/incredible_proof_machine/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Independence_CH</title>
       <link>/theories/independence_ch/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/independence_ch/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Inductive_Confidentiality</title>
       <link>/theories/inductive_confidentiality/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/inductive_confidentiality/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Inductive_Inference</title>
       <link>/theories/inductive_inference/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/inductive_inference/</guid>
       <description></description>
     </item>
     
     <item>
       <title>InformationFlowSlicing</title>
       <link>/theories/informationflowslicing/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/informationflowslicing/</guid>
       <description></description>
     </item>
     
     <item>
       <title>InformationFlowSlicing_Inter</title>
       <link>/theories/informationflowslicing_inter/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/informationflowslicing_inter/</guid>
       <description></description>
     </item>
     
     <item>
       <title>InfPathElimination</title>
       <link>/theories/infpathelimination/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/infpathelimination/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Integration</title>
       <link>/theories/integration/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/integration/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Interpolation_Polynomials_HOL_Algebra</title>
       <link>/theories/interpolation_polynomials_hol_algebra/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/interpolation_polynomials_hol_algebra/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Interpreter_Optimizations</title>
       <link>/theories/interpreter_optimizations/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/interpreter_optimizations/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Interval_Arithmetic_Word32</title>
       <link>/theories/interval_arithmetic_word32/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/interval_arithmetic_word32/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Intro_Dest_Elim</title>
       <link>/theories/intro_dest_elim/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/intro_dest_elim/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Involutions2Squares</title>
       <link>/theories/involutions2squares/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/involutions2squares/</guid>
       <description></description>
     </item>
     
     <item>
       <title>IP_Addresses</title>
       <link>/theories/ip_addresses/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/ip_addresses/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Iptables_Semantics</title>
       <link>/theories/iptables_semantics/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/iptables_semantics/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Iptables_Semantics_Examples</title>
       <link>/theories/iptables_semantics_examples/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/iptables_semantics_examples/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Iptables_Semantics_Examples_Big</title>
       <link>/theories/iptables_semantics_examples_big/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/iptables_semantics_examples_big/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Irrational_Series_Erdos_Straus</title>
       <link>/theories/irrational_series_erdos_straus/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/irrational_series_erdos_straus/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Irrationality_J_Hancl</title>
       <link>/theories/irrationality_j_hancl/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/irrationality_j_hancl/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Irrationals_From_THEBOOK</title>
       <link>/theories/irrationals_from_thebook/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/irrationals_from_thebook/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Isabelle_C</title>
       <link>/theories/isabelle_c/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/isabelle_c/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Isabelle_Marries_Dirac</title>
       <link>/theories/isabelle_marries_dirac/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/isabelle_marries_dirac/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Isabelle_Meta_Model</title>
       <link>/theories/isabelle_meta_model/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/isabelle_meta_model/</guid>
       <description></description>
     </item>
     
     <item>
       <title>IsaGeoCoq</title>
       <link>/theories/isageocoq/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/isageocoq/</guid>
       <description></description>
     </item>
     
     <item>
       <title>IsaNet</title>
       <link>/theories/isanet/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/isanet/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Jacobson_Basic_Algebra</title>
       <link>/theories/jacobson_basic_algebra/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/jacobson_basic_algebra/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Jinja</title>
       <link>/theories/jinja/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/jinja/</guid>
       <description></description>
     </item>
     
     <item>
       <title>JinjaDCI</title>
       <link>/theories/jinjadci/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/jinjadci/</guid>
       <description></description>
     </item>
     
     <item>
       <title>JinjaThreads</title>
       <link>/theories/jinjathreads/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/jinjathreads/</guid>
       <description></description>
     </item>
     
     <item>
       <title>JiveDataStoreModel</title>
       <link>/theories/jivedatastoremodel/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/jivedatastoremodel/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Jordan_Hoelder</title>
       <link>/theories/jordan_hoelder/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/jordan_hoelder/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Jordan_Normal_Form</title>
       <link>/theories/jordan_normal_form/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/jordan_normal_form/</guid>
       <description></description>
     </item>
     
     <item>
       <title>KAD</title>
       <link>/theories/kad/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/kad/</guid>
       <description></description>
     </item>
     
     <item>
       <title>KAT_and_DRA</title>
       <link>/theories/kat_and_dra/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/kat_and_dra/</guid>
       <description></description>
     </item>
     
     <item>
       <title>KBPs</title>
       <link>/theories/kbps/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/kbps/</guid>
       <description></description>
     </item>
     
     <item>
       <title>KD_Tree</title>
       <link>/theories/kd_tree/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/kd_tree/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Key_Agreement_Strong_Adversaries</title>
       <link>/theories/key_agreement_strong_adversaries/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/key_agreement_strong_adversaries/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Khovanskii_Theorem</title>
       <link>/theories/khovanskii_theorem/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/khovanskii_theorem/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Kleene_Algebra</title>
       <link>/theories/kleene_algebra/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/kleene_algebra/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Knights_Tour</title>
       <link>/theories/knights_tour/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/knights_tour/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Knot_Theory</title>
       <link>/theories/knot_theory/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/knot_theory/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Knuth_Bendix_Order</title>
       <link>/theories/knuth_bendix_order/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/knuth_bendix_order/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Knuth_Morris_Pratt</title>
       <link>/theories/knuth_morris_pratt/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/knuth_morris_pratt/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Koenigsberg_Friendship</title>
       <link>/theories/koenigsberg_friendship/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/koenigsberg_friendship/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Kruskal</title>
       <link>/theories/kruskal/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/kruskal/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Kuratowski_Closure_Complement</title>
       <link>/theories/kuratowski_closure_complement/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/kuratowski_closure_complement/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Lam-ml-Normalization</title>
       <link>/theories/lam-ml-normalization/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/lam-ml-normalization/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Lambda_Free_EPO</title>
       <link>/theories/lambda_free_epo/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/lambda_free_epo/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Lambda_Free_KBOs</title>
       <link>/theories/lambda_free_kbos/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/lambda_free_kbos/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Lambda_Free_RPOs</title>
       <link>/theories/lambda_free_rpos/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/lambda_free_rpos/</guid>
       <description></description>
     </item>
     
     <item>
       <title>LambdaAuth</title>
       <link>/theories/lambdaauth/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/lambdaauth/</guid>
       <description></description>
     </item>
     
     <item>
       <title>LambdaMu</title>
       <link>/theories/lambdamu/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/lambdamu/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Lambert_W</title>
       <link>/theories/lambert_w/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/lambert_w/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Landau_Symbols</title>
       <link>/theories/landau_symbols/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/landau_symbols/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Laplace_Transform</title>
       <link>/theories/laplace_transform/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/laplace_transform/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Latin_Square</title>
       <link>/theories/latin_square/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/latin_square/</guid>
       <description></description>
     </item>
     
     <item>
       <title>LatticeProperties</title>
       <link>/theories/latticeproperties/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/latticeproperties/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Launchbury</title>
       <link>/theories/launchbury/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/launchbury/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Laws_of_Large_Numbers</title>
       <link>/theories/laws_of_large_numbers/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/laws_of_large_numbers/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Lazy-Lists-II</title>
       <link>/theories/lazy-lists-ii/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/lazy-lists-ii/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Lazy_Case</title>
       <link>/theories/lazy_case/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/lazy_case/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Lehmer</title>
       <link>/theories/lehmer/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/lehmer/</guid>
       <description></description>
     </item>
     
     <item>
       <title>LEM</title>
       <link>/theories/lem/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/lem/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Lifting_Definition_Option</title>
       <link>/theories/lifting_definition_option/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/lifting_definition_option/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Lifting_the_Exponent</title>
       <link>/theories/lifting_the_exponent/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/lifting_the_exponent/</guid>
       <description></description>
     </item>
     
     <item>
       <title>LightweightJava</title>
       <link>/theories/lightweightjava/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/lightweightjava/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Linear_Inequalities</title>
       <link>/theories/linear_inequalities/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/linear_inequalities/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Linear_Programming</title>
       <link>/theories/linear_programming/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/linear_programming/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Linear_Recurrences</title>
       <link>/theories/linear_recurrences/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/linear_recurrences/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Linear_Recurrences_Solver</title>
       <link>/theories/linear_recurrences_solver/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/linear_recurrences_solver/</guid>
       <description></description>
     </item>
     
     <item>
       <title>LinearQuantifierElim</title>
       <link>/theories/linearquantifierelim/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/linearquantifierelim/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Liouville_Numbers</title>
       <link>/theories/liouville_numbers/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/liouville_numbers/</guid>
       <description></description>
     </item>
     
     <item>
       <title>List-Index</title>
       <link>/theories/list-index/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/list-index/</guid>
       <description></description>
     </item>
     
     <item>
       <title>List-Infinite</title>
       <link>/theories/list-infinite/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/list-infinite/</guid>
       <description></description>
     </item>
     
     <item>
       <title>List_Interleaving</title>
       <link>/theories/list_interleaving/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/list_interleaving/</guid>
       <description></description>
     </item>
     
     <item>
       <title>List_Inversions</title>
       <link>/theories/list_inversions/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/list_inversions/</guid>
       <description></description>
     </item>
     
     <item>
       <title>List_Update</title>
       <link>/theories/list_update/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/list_update/</guid>
       <description></description>
     </item>
     
     <item>
       <title>LLL_Basis_Reduction</title>
       <link>/theories/lll_basis_reduction/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/lll_basis_reduction/</guid>
       <description></description>
     </item>
     
     <item>
       <title>LLL_Factorization</title>
       <link>/theories/lll_factorization/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/lll_factorization/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Localization_Ring</title>
       <link>/theories/localization_ring/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/localization_ring/</guid>
       <description></description>
     </item>
     
     <item>
       <title>LocalLexing</title>
       <link>/theories/locallexing/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/locallexing/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Locally-Nameless-Sigma</title>
       <link>/theories/locally-nameless-sigma/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/locally-nameless-sigma/</guid>
       <description></description>
     </item>
     
     <item>
       <title>LOFT</title>
       <link>/theories/loft/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/loft/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Logging_Independent_Anonymity</title>
       <link>/theories/logging_independent_anonymity/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/logging_independent_anonymity/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Lorenz_Approximation</title>
       <link>/theories/lorenz_approximation/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/lorenz_approximation/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Lorenz_C0</title>
       <link>/theories/lorenz_c0/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/lorenz_c0/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Lorenz_C1</title>
       <link>/theories/lorenz_c1/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/lorenz_c1/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Lowe_Ontological_Argument</title>
       <link>/theories/lowe_ontological_argument/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/lowe_ontological_argument/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Lower_Semicontinuous</title>
       <link>/theories/lower_semicontinuous/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/lower_semicontinuous/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Lp</title>
       <link>/theories/lp/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/lp/</guid>
       <description></description>
     </item>
     
     <item>
       <title>LP_Duality</title>
       <link>/theories/lp_duality/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/lp_duality/</guid>
       <description></description>
     </item>
     
     <item>
       <title>LTL</title>
       <link>/theories/ltl/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/ltl/</guid>
       <description></description>
     </item>
     
     <item>
       <title>LTL_Master_Theorem</title>
       <link>/theories/ltl_master_theorem/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/ltl_master_theorem/</guid>
       <description></description>
     </item>
     
     <item>
       <title>LTL_Normal_Form</title>
       <link>/theories/ltl_normal_form/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/ltl_normal_form/</guid>
       <description></description>
     </item>
     
     <item>
       <title>LTL_to_DRA</title>
       <link>/theories/ltl_to_dra/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/ltl_to_dra/</guid>
       <description></description>
     </item>
     
     <item>
       <title>LTL_to_GBA</title>
       <link>/theories/ltl_to_gba/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/ltl_to_gba/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Lucas_Theorem</title>
       <link>/theories/lucas_theorem/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/lucas_theorem/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Markov_Models</title>
       <link>/theories/markov_models/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/markov_models/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Marriage</title>
       <link>/theories/marriage/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/marriage/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Mason_Stothers</title>
       <link>/theories/mason_stothers/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/mason_stothers/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Matrices_for_ODEs</title>
       <link>/theories/matrices_for_odes/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/matrices_for_odes/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Matrix</title>
       <link>/theories/matrix/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/matrix/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Matrix_Tensor</title>
       <link>/theories/matrix_tensor/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/matrix_tensor/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Matroids</title>
       <link>/theories/matroids/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/matroids/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Max-Card-Matching</title>
       <link>/theories/max-card-matching/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/max-card-matching/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Maximum_Segment_Sum</title>
       <link>/theories/maximum_segment_sum/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/maximum_segment_sum/</guid>
       <description></description>
     </item>
     
     <item>
       <title>MDP-Algorithms</title>
       <link>/theories/mdp-algorithms/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/mdp-algorithms/</guid>
       <description></description>
     </item>
     
     <item>
       <title>MDP-Rewards</title>
       <link>/theories/mdp-rewards/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/mdp-rewards/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Median_Method</title>
       <link>/theories/median_method/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/median_method/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Median_Of_Medians_Selection</title>
       <link>/theories/median_of_medians_selection/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/median_of_medians_selection/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Menger</title>
       <link>/theories/menger/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/menger/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Mereology</title>
       <link>/theories/mereology/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/mereology/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Mersenne_Primes</title>
       <link>/theories/mersenne_primes/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/mersenne_primes/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Metalogic_ProofChecker</title>
       <link>/theories/metalogic_proofchecker/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/metalogic_proofchecker/</guid>
       <description></description>
     </item>
     
     <item>
       <title>MFMC_Countable</title>
       <link>/theories/mfmc_countable/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/mfmc_countable/</guid>
       <description></description>
     </item>
     
     <item>
       <title>MFODL_Monitor_Optimized</title>
       <link>/theories/mfodl_monitor_optimized/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/mfodl_monitor_optimized/</guid>
       <description></description>
     </item>
     
     <item>
       <title>MFOTL_Monitor</title>
       <link>/theories/mfotl_monitor/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/mfotl_monitor/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Minimal_SSA</title>
       <link>/theories/minimal_ssa/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/minimal_ssa/</guid>
       <description></description>
     </item>
     
     <item>
       <title>MiniML</title>
       <link>/theories/miniml/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/miniml/</guid>
       <description></description>
     </item>
     
     <item>
       <title>MiniSail</title>
       <link>/theories/minisail/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/minisail/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Minkowskis_Theorem</title>
       <link>/theories/minkowskis_theorem/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/minkowskis_theorem/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Minsky_Machines</title>
       <link>/theories/minsky_machines/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/minsky_machines/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Modal_Logics_for_NTS</title>
       <link>/theories/modal_logics_for_nts/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/modal_logics_for_nts/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Modular_arithmetic_LLL_and_HNF_algorithms</title>
       <link>/theories/modular_arithmetic_lll_and_hnf_algorithms/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/modular_arithmetic_lll_and_hnf_algorithms/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Modular_Assembly_Kit_Security</title>
       <link>/theories/modular_assembly_kit_security/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/modular_assembly_kit_security/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Monad_Memo_DP</title>
       <link>/theories/monad_memo_dp/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/monad_memo_dp/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Monad_Normalisation</title>
       <link>/theories/monad_normalisation/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/monad_normalisation/</guid>
       <description></description>
     </item>
     
     <item>
       <title>MonoBoolTranAlgebra</title>
       <link>/theories/monobooltranalgebra/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/monobooltranalgebra/</guid>
       <description></description>
     </item>
     
     <item>
       <title>MonoidalCategory</title>
       <link>/theories/monoidalcategory/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/monoidalcategory/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Monomorphic_Monad</title>
       <link>/theories/monomorphic_monad/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/monomorphic_monad/</guid>
       <description></description>
     </item>
     
     <item>
       <title>MSO_Regex_Equivalence</title>
       <link>/theories/mso_regex_equivalence/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/mso_regex_equivalence/</guid>
       <description></description>
     </item>
     
     <item>
       <title>MuchAdoAboutTwo</title>
       <link>/theories/muchadoabouttwo/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/muchadoabouttwo/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Multi_Party_Computation</title>
       <link>/theories/multi_party_computation/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/multi_party_computation/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Multirelations</title>
       <link>/theories/multirelations/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/multirelations/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Multiset_Ordering_NPC</title>
       <link>/theories/multiset_ordering_npc/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/multiset_ordering_npc/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Myhill-Nerode</title>
       <link>/theories/myhill-nerode/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/myhill-nerode/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Name_Carrying_Type_Inference</title>
       <link>/theories/name_carrying_type_inference/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/name_carrying_type_inference/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Nano_JSON</title>
       <link>/theories/nano_json/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/nano_json/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Nash_Williams</title>
       <link>/theories/nash_williams/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/nash_williams/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Nat-Interval-Logic</title>
       <link>/theories/nat-interval-logic/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/nat-interval-logic/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Native_Word</title>
       <link>/theories/native_word/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/native_word/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Nested_Multisets_Ordinals</title>
       <link>/theories/nested_multisets_ordinals/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/nested_multisets_ordinals/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Network_Security_Policy_Verification</title>
       <link>/theories/network_security_policy_verification/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/network_security_policy_verification/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Neumann_Morgenstern_Utility</title>
       <link>/theories/neumann_morgenstern_utility/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/neumann_morgenstern_utility/</guid>
       <description></description>
     </item>
     
     <item>
       <title>No_FTL_observers</title>
       <link>/theories/no_ftl_observers/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/no_ftl_observers/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Nominal2</title>
       <link>/theories/nominal2/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/nominal2/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Noninterference_Concurrent_Composition</title>
       <link>/theories/noninterference_concurrent_composition/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/noninterference_concurrent_composition/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Noninterference_CSP</title>
       <link>/theories/noninterference_csp/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/noninterference_csp/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Noninterference_Generic_Unwinding</title>
       <link>/theories/noninterference_generic_unwinding/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/noninterference_generic_unwinding/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Noninterference_Inductive_Unwinding</title>
       <link>/theories/noninterference_inductive_unwinding/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/noninterference_inductive_unwinding/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Noninterference_Ipurge_Unwinding</title>
       <link>/theories/noninterference_ipurge_unwinding/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/noninterference_ipurge_unwinding/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Noninterference_Sequential_Composition</title>
       <link>/theories/noninterference_sequential_composition/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/noninterference_sequential_composition/</guid>
       <description></description>
     </item>
     
     <item>
       <title>NormByEval</title>
       <link>/theories/normbyeval/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/normbyeval/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Nullstellensatz</title>
       <link>/theories/nullstellensatz/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/nullstellensatz/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Number_Theoretic_Transform</title>
       <link>/theories/number_theoretic_transform/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/number_theoretic_transform/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Octonions</title>
       <link>/theories/octonions/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/octonions/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Old_Datatype_Show</title>
       <link>/theories/old_datatype_show/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/old_datatype_show/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Open_Induction</title>
       <link>/theories/open_induction/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/open_induction/</guid>
       <description></description>
     </item>
     
     <item>
       <title>OpSets</title>
       <link>/theories/opsets/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/opsets/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Optics</title>
       <link>/theories/optics/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/optics/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Optimal_BST</title>
       <link>/theories/optimal_bst/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/optimal_bst/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Orbit_Stabiliser</title>
       <link>/theories/orbit_stabiliser/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/orbit_stabiliser/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Order_Lattice_Props</title>
       <link>/theories/order_lattice_props/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/order_lattice_props/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Ordered_Resolution_Prover</title>
       <link>/theories/ordered_resolution_prover/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/ordered_resolution_prover/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Ordinal</title>
       <link>/theories/ordinal/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/ordinal/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Ordinal_Partitions</title>
       <link>/theories/ordinal_partitions/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/ordinal_partitions/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Ordinals_and_Cardinals</title>
       <link>/theories/ordinals_and_cardinals/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/ordinals_and_cardinals/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Ordinary_Differential_Equations</title>
       <link>/theories/ordinary_differential_equations/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/ordinary_differential_equations/</guid>
       <description></description>
     </item>
     
     <item>
       <title>PAC_Checker</title>
       <link>/theories/pac_checker/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/pac_checker/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Package_logic</title>
       <link>/theories/package_logic/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/package_logic/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Padic_Field</title>
       <link>/theories/padic_field/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/padic_field/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Padic_Ints</title>
       <link>/theories/padic_ints/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/padic_ints/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Pairing_Heap</title>
       <link>/theories/pairing_heap/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/pairing_heap/</guid>
       <description></description>
     </item>
     
     <item>
       <title>PAL</title>
       <link>/theories/pal/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/pal/</guid>
       <description></description>
     </item>
     
     <item>
       <title>PAPP_Impossibility</title>
       <link>/theories/papp_impossibility/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/papp_impossibility/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Paraconsistency</title>
       <link>/theories/paraconsistency/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/paraconsistency/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Parity_Game</title>
       <link>/theories/parity_game/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/parity_game/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Partial_Function_MR</title>
       <link>/theories/partial_function_mr/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/partial_function_mr/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Partial_Order_Reduction</title>
       <link>/theories/partial_order_reduction/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/partial_order_reduction/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Password_Authentication_Protocol</title>
       <link>/theories/password_authentication_protocol/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/password_authentication_protocol/</guid>
       <description></description>
     </item>
     
     <item>
       <title>PCF</title>
       <link>/theories/pcf/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/pcf/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Pell</title>
       <link>/theories/pell/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/pell/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Perfect-Number-Thm</title>
       <link>/theories/perfect-number-thm/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/perfect-number-thm/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Perron_Frobenius</title>
       <link>/theories/perron_frobenius/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/perron_frobenius/</guid>
       <description></description>
     </item>
     
     <item>
       <title>pGCL</title>
       <link>/theories/pgcl/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/pgcl/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Physical_Quantities</title>
       <link>/theories/physical_quantities/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/physical_quantities/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Pi_Calculus</title>
       <link>/theories/pi_calculus/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/pi_calculus/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Pi_Transcendental</title>
       <link>/theories/pi_transcendental/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/pi_transcendental/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Planarity_Certificates</title>
       <link>/theories/planarity_certificates/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/planarity_certificates/</guid>
       <description></description>
     </item>
     
     <item>
       <title>PLM</title>
       <link>/theories/plm/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/plm/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Pluennecke_Ruzsa_Inequality</title>
       <link>/theories/pluennecke_ruzsa_inequality/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/pluennecke_ruzsa_inequality/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Poincare_Bendixson</title>
       <link>/theories/poincare_bendixson/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/poincare_bendixson/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Poincare_Disc</title>
       <link>/theories/poincare_disc/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/poincare_disc/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Polynomial_Factorization</title>
       <link>/theories/polynomial_factorization/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/polynomial_factorization/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Polynomial_Interpolation</title>
       <link>/theories/polynomial_interpolation/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/polynomial_interpolation/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Polynomials</title>
       <link>/theories/polynomials/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/polynomials/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Pop_Refinement</title>
       <link>/theories/pop_refinement/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/pop_refinement/</guid>
       <description></description>
     </item>
     
     <item>
       <title>POPLmark-deBruijn</title>
       <link>/theories/poplmark-debruijn/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/poplmark-debruijn/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Posix-Lexing</title>
       <link>/theories/posix-lexing/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/posix-lexing/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Possibilistic_Noninterference</title>
       <link>/theories/possibilistic_noninterference/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/possibilistic_noninterference/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Power_Sum_Polynomials</title>
       <link>/theories/power_sum_polynomials/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/power_sum_polynomials/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Pratt_Certificate</title>
       <link>/theories/pratt_certificate/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/pratt_certificate/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Prefix_Free_Code_Combinators</title>
       <link>/theories/prefix_free_code_combinators/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/prefix_free_code_combinators/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Presburger-Automata</title>
       <link>/theories/presburger-automata/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/presburger-automata/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Prim_Dijkstra_Simple</title>
       <link>/theories/prim_dijkstra_simple/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/prim_dijkstra_simple/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Prime_Distribution_Elementary</title>
       <link>/theories/prime_distribution_elementary/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/prime_distribution_elementary/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Prime_Harmonic_Series</title>
       <link>/theories/prime_harmonic_series/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/prime_harmonic_series/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Prime_Number_Theorem</title>
       <link>/theories/prime_number_theorem/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/prime_number_theorem/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Priority_Queue_Braun</title>
       <link>/theories/priority_queue_braun/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/priority_queue_braun/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Priority_Search_Trees</title>
       <link>/theories/priority_search_trees/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/priority_search_trees/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Probabilistic_Noninterference</title>
       <link>/theories/probabilistic_noninterference/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/probabilistic_noninterference/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Probabilistic_Prime_Tests</title>
       <link>/theories/probabilistic_prime_tests/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/probabilistic_prime_tests/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Probabilistic_System_Zoo</title>
       <link>/theories/probabilistic_system_zoo/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/probabilistic_system_zoo/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Probabilistic_Timed_Automata</title>
       <link>/theories/probabilistic_timed_automata/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/probabilistic_timed_automata/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Probabilistic_While</title>
       <link>/theories/probabilistic_while/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/probabilistic_while/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Program-Conflict-Analysis</title>
       <link>/theories/program-conflict-analysis/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/program-conflict-analysis/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Progress_Tracking</title>
       <link>/theories/progress_tracking/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/progress_tracking/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Projective_Geometry</title>
       <link>/theories/projective_geometry/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/projective_geometry/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Projective_Measurements</title>
       <link>/theories/projective_measurements/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/projective_measurements/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Promela</title>
       <link>/theories/promela/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/promela/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Proof_Strategy_Language</title>
       <link>/theories/proof_strategy_language/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/proof_strategy_language/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Propositional_Proof_Systems</title>
       <link>/theories/propositional_proof_systems/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/propositional_proof_systems/</guid>
       <description></description>
     </item>
     
     <item>
       <title>PropResPI</title>
       <link>/theories/proprespi/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/proprespi/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Prpu_Maxflow</title>
       <link>/theories/prpu_maxflow/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/prpu_maxflow/</guid>
       <description></description>
     </item>
     
     <item>
       <title>PSemigroupsConvolution</title>
       <link>/theories/psemigroupsconvolution/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/psemigroupsconvolution/</guid>
       <description></description>
     </item>
     
     <item>
       <title>PseudoHoops</title>
       <link>/theories/pseudohoops/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/pseudohoops/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Psi_Calculi</title>
       <link>/theories/psi_calculi/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/psi_calculi/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Ptolemys_Theorem</title>
       <link>/theories/ptolemys_theorem/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/ptolemys_theorem/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Public_Announcement_Logic</title>
       <link>/theories/public_announcement_logic/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/public_announcement_logic/</guid>
       <description></description>
     </item>
     
     <item>
       <title>QHLProver</title>
       <link>/theories/qhlprover/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/qhlprover/</guid>
       <description></description>
     </item>
     
     <item>
       <title>QR_Decomposition</title>
       <link>/theories/qr_decomposition/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/qr_decomposition/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Quantales</title>
       <link>/theories/quantales/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/quantales/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Quasi_Borel_Spaces</title>
       <link>/theories/quasi_borel_spaces/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/quasi_borel_spaces/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Quaternions</title>
       <link>/theories/quaternions/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/quaternions/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Query_Optimization</title>
       <link>/theories/query_optimization/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/query_optimization/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Quick_Sort_Cost</title>
       <link>/theories/quick_sort_cost/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/quick_sort_cost/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Ramsey-Infinite</title>
       <link>/theories/ramsey-infinite/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/ramsey-infinite/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Random_BSTs</title>
       <link>/theories/random_bsts/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/random_bsts/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Random_Graph_Subgraph_Threshold</title>
       <link>/theories/random_graph_subgraph_threshold/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/random_graph_subgraph_threshold/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Randomised_BSTs</title>
       <link>/theories/randomised_bsts/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/randomised_bsts/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Randomised_Social_Choice</title>
       <link>/theories/randomised_social_choice/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/randomised_social_choice/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Rank_Nullity_Theorem</title>
       <link>/theories/rank_nullity_theorem/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/rank_nullity_theorem/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Real_Impl</title>
       <link>/theories/real_impl/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/real_impl/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Real_Power</title>
       <link>/theories/real_power/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/real_power/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Real_Time_Deque</title>
       <link>/theories/real_time_deque/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/real_time_deque/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Recursion-Addition</title>
       <link>/theories/recursion-addition/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/recursion-addition/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Recursion-Theory-I</title>
       <link>/theories/recursion-theory-i/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/recursion-theory-i/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Refine_Imperative_HOL</title>
       <link>/theories/refine_imperative_hol/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/refine_imperative_hol/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Refine_Monadic</title>
       <link>/theories/refine_monadic/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/refine_monadic/</guid>
       <description></description>
     </item>
     
     <item>
       <title>RefinementReactive</title>
       <link>/theories/refinementreactive/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/refinementreactive/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Regex_Equivalence</title>
       <link>/theories/regex_equivalence/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/regex_equivalence/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Registers</title>
       <link>/theories/registers/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/registers/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Regression_Test_Selection</title>
       <link>/theories/regression_test_selection/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/regression_test_selection/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Regular-Sets</title>
       <link>/theories/regular-sets/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/regular-sets/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Regular_Algebras</title>
       <link>/theories/regular_algebras/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/regular_algebras/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Regular_Tree_Relations</title>
       <link>/theories/regular_tree_relations/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/regular_tree_relations/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Relation_Algebra</title>
       <link>/theories/relation_algebra/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/relation_algebra/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Relational-Incorrectness-Logic</title>
       <link>/theories/relational-incorrectness-logic/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/relational-incorrectness-logic/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Relational_Disjoint_Set_Forests</title>
       <link>/theories/relational_disjoint_set_forests/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/relational_disjoint_set_forests/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Relational_Forests</title>
       <link>/theories/relational_forests/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/relational_forests/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Relational_Method</title>
       <link>/theories/relational_method/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/relational_method/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Relational_Minimum_Spanning_Trees</title>
       <link>/theories/relational_minimum_spanning_trees/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/relational_minimum_spanning_trees/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Relational_Paths</title>
       <link>/theories/relational_paths/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/relational_paths/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Rep_Fin_Groups</title>
       <link>/theories/rep_fin_groups/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/rep_fin_groups/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Residuated_Lattices</title>
       <link>/theories/residuated_lattices/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/residuated_lattices/</guid>
       <description></description>
     </item>
     
     <item>
       <title>ResiduatedTransitionSystem</title>
       <link>/theories/residuatedtransitionsystem/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/residuatedtransitionsystem/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Resolution_FOL</title>
       <link>/theories/resolution_fol/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/resolution_fol/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Rewrite_Properties_Reduction</title>
       <link>/theories/rewrite_properties_reduction/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/rewrite_properties_reduction/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Rewriting_Z</title>
       <link>/theories/rewriting_z/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/rewriting_z/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Ribbon_Proofs</title>
       <link>/theories/ribbon_proofs/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/ribbon_proofs/</guid>
       <description></description>
     </item>
     
     <item>
       <title>RIPEMD-160-SPARK</title>
       <link>/theories/ripemd-160-spark/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/ripemd-160-spark/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Risk_Free_Lending</title>
       <link>/theories/risk_free_lending/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/risk_free_lending/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Robbins-Conjecture</title>
       <link>/theories/robbins-conjecture/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/robbins-conjecture/</guid>
       <description></description>
     </item>
     
     <item>
       <title>ROBDD</title>
       <link>/theories/robdd/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/robdd/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Robinson_Arithmetic</title>
       <link>/theories/robinson_arithmetic/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/robinson_arithmetic/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Root_Balanced_Tree</title>
       <link>/theories/root_balanced_tree/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/root_balanced_tree/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Roth_Arithmetic_Progressions</title>
       <link>/theories/roth_arithmetic_progressions/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/roth_arithmetic_progressions/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Routing</title>
       <link>/theories/routing/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/routing/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Roy_Floyd_Warshall</title>
       <link>/theories/roy_floyd_warshall/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/roy_floyd_warshall/</guid>
       <description></description>
     </item>
     
     <item>
       <title>RSAPSS</title>
       <link>/theories/rsapss/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/rsapss/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Safe_Distance</title>
       <link>/theories/safe_distance/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/safe_distance/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Safe_OCL</title>
       <link>/theories/safe_ocl/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/safe_ocl/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Safe_Range_RC</title>
       <link>/theories/safe_range_rc/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/safe_range_rc/</guid>
       <description></description>
     </item>
     
     <item>
       <title>SATSolverVerification</title>
       <link>/theories/satsolververification/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/satsolververification/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Saturation_Framework</title>
       <link>/theories/saturation_framework/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/saturation_framework/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Saturation_Framework_Extensions</title>
       <link>/theories/saturation_framework_extensions/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/saturation_framework_extensions/</guid>
       <description></description>
     </item>
     
     <item>
       <title>SC_DOM_Components</title>
       <link>/theories/sc_dom_components/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/sc_dom_components/</guid>
       <description></description>
     </item>
     
     <item>
       <title>SCC_Bloemen_Sequential</title>
       <link>/theories/scc_bloemen_sequential/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/scc_bloemen_sequential/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Schutz_Spacetime</title>
       <link>/theories/schutz_spacetime/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/schutz_spacetime/</guid>
       <description></description>
     </item>
     
     <item>
       <title>SDS_Impossibility</title>
       <link>/theories/sds_impossibility/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/sds_impossibility/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Search the Archive</title>
       <link>/search/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/search/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Secondary_Sylow</title>
       <link>/theories/secondary_sylow/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/secondary_sylow/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Security_Protocol_Refinement</title>
       <link>/theories/security_protocol_refinement/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/security_protocol_refinement/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Selection_Heap_Sort</title>
       <link>/theories/selection_heap_sort/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/selection_heap_sort/</guid>
       <description></description>
     </item>
     
     <item>
       <title>SenSocialChoice</title>
       <link>/theories/sensocialchoice/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/sensocialchoice/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Separata</title>
       <link>/theories/separata/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/separata/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Separation_Algebra</title>
       <link>/theories/separation_algebra/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/separation_algebra/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Separation_Logic_Imperative_HOL</title>
       <link>/theories/separation_logic_imperative_hol/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/separation_logic_imperative_hol/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Separation_Logic_Unbounded</title>
       <link>/theories/separation_logic_unbounded/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/separation_logic_unbounded/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Sepref_Basic</title>
       <link>/theories/sepref_basic/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/sepref_basic/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Sepref_IICF</title>
       <link>/theories/sepref_iicf/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/sepref_iicf/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Sepref_Prereq</title>
       <link>/theories/sepref_prereq/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/sepref_prereq/</guid>
       <description></description>
     </item>
     
     <item>
       <title>SequentInvertibility</title>
       <link>/theories/sequentinvertibility/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/sequentinvertibility/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Shadow_DOM</title>
       <link>/theories/shadow_dom/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/shadow_dom/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Shadow_SC_DOM</title>
       <link>/theories/shadow_sc_dom/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/shadow_sc_dom/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Shivers-CFA</title>
       <link>/theories/shivers-cfa/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/shivers-cfa/</guid>
       <description></description>
     </item>
     
     <item>
       <title>ShortestPath</title>
       <link>/theories/shortestpath/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/shortestpath/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Show</title>
       <link>/theories/show/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/show/</guid>
       <description></description>
     </item>
     
     <item>
       <title>SIFPL</title>
       <link>/theories/sifpl/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/sifpl/</guid>
       <description></description>
     </item>
     
     <item>
       <title>SIFUM_Type_Systems</title>
       <link>/theories/sifum_type_systems/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/sifum_type_systems/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Sigma_Commit_Crypto</title>
       <link>/theories/sigma_commit_crypto/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/sigma_commit_crypto/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Signature_Groebner</title>
       <link>/theories/signature_groebner/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/signature_groebner/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Simpl</title>
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     <item>
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     <item>
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     <item>
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     <item>
       <title>SimplifiedOntologicalArgument</title>
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     <item>
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       <guid>/theories/skew_heap/</guid>
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     <item>
       <title>Skip_Lists</title>
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       <guid>/theories/skip_lists/</guid>
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     <item>
       <title>Slicing</title>
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       <guid>/theories/slicing/</guid>
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     <item>
       <title>Sliding_Window_Algorithm</title>
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       <guid>/theories/sliding_window_algorithm/</guid>
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     </item>
     
     <item>
       <title>SM</title>
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       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/sm/</guid>
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     </item>
     
     <item>
       <title>SM_Base</title>
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       <guid>/theories/sm_base/</guid>
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     </item>
     
     <item>
       <title>Smith_Normal_Form</title>
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       <guid>/theories/smith_normal_form/</guid>
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     </item>
     
     <item>
       <title>Smooth_Manifolds</title>
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       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/smooth_manifolds/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Solidity</title>
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       <guid>/theories/solidity/</guid>
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     <item>
       <title>Sophomores_Dream</title>
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       <guid>/theories/sophomores_dream/</guid>
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     <item>
       <title>Sort_Encodings</title>
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     <item>
       <title>Source_Coding_Theorem</title>
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       <guid>/theories/source_coding_theorem/</guid>
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     </item>
     
     <item>
       <title>SPARCv8</title>
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       <guid>/theories/sparcv8/</guid>
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     <item>
       <title>SpecCheck</title>
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       <guid>/theories/speccheck/</guid>
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     <item>
       <title>Special_Function_Bounds</title>
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       <guid>/theories/special_function_bounds/</guid>
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     <item>
       <title>Splay_Tree</title>
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       <guid>/theories/splay_tree/</guid>
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     <item>
       <title>Sqrt_Babylonian</title>
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     <item>
       <title>Stable_Matching</title>
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       <guid>/theories/stable_matching/</guid>
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     <item>
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     <item>
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     <item>
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     <item>
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     </item>
     
     <item>
       <title>Stellar_Quorums</title>
       <link>/theories/stellar_quorums/</link>
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     <item>
       <title>Stern_Brocot</title>
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     <item>
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     <item>
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     <item>
       <title>Stochastic_Matrices</title>
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       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/stochastic_matrices/</guid>
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     </item>
     
     <item>
       <title>Stone_Algebras</title>
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     <item>
       <title>Stone_Kleene_Relation_Algebras</title>
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     <item>
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     <item>
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       <guid>/theories/store_buffer_reduction/</guid>
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     <item>
       <title>Stream-Fusion</title>
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       <guid>/theories/stream-fusion/</guid>
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     <item>
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     <item>
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     <item>
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       <guid>/theories/sturm_sequences/</guid>
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     <item>
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       <guid>/theories/sturm_tarski/</guid>
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     </item>
     
     <item>
       <title>Stuttering_Equivalence</title>
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       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/stuttering_equivalence/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Submission</title>
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     <item>
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     <item>
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       <guid>/theories/subresultants/</guid>
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     </item>
     
     <item>
       <title>Subset_Boolean_Algebras</title>
       <link>/theories/subset_boolean_algebras/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/subset_boolean_algebras/</guid>
       <description></description>
     </item>
     
     <item>
       <title>SumSquares</title>
       <link>/theories/sumsquares/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/sumsquares/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Sunflowers</title>
       <link>/theories/sunflowers/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/sunflowers/</guid>
       <description></description>
     </item>
     
     <item>
       <title>SuperCalc</title>
       <link>/theories/supercalc/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/supercalc/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Surprise_Paradox</title>
       <link>/theories/surprise_paradox/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/surprise_paradox/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Symmetric_Polynomials</title>
       <link>/theories/symmetric_polynomials/</link>
       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/symmetric_polynomials/</guid>
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     </item>
     
     <item>
       <title>Syntax_Independent_Logic</title>
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       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/syntax_independent_logic/</guid>
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     </item>
     
     <item>
       <title>Szemeredi_Regularity</title>
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       <guid>/theories/szemeredi_regularity/</guid>
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     <item>
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       <guid>/theories/szpilrajn/</guid>
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     <item>
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       <guid>/theories/tail_recursive_functions/</guid>
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     <item>
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     <item>
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       <guid>/theories/taylor_models/</guid>
       <description></description>
     </item>
     
     <item>
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       <pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate>
       
       <guid>/theories/tesl_language/</guid>
       <description></description>
     </item>
     
     <item>
       <title>Three_Circles</title>
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       <guid>/theories/three_circles/</guid>
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     <item>
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       <guid>/theories/timed_automata/</guid>
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     </item>
     
     <item>
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       <guid>/theories/tla/</guid>
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     <item>
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     <item>
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     <item>
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       <guid>/theories/tortoisehare/</guid>
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     <item>
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     <item>
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     <item>
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     <item>
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     <item>
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     <item>
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     <item>
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     <item>
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     <item>
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     <item>
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     <item>
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     <item>
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     <item>
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     <item>
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-<meta property="og:description" content="712 Entries   436 Authors   ~226,200 Lemmas   ~3,664,200 Lines of Code   Most used AFP entries:   Name Used by ? entries   1. List-Index 22   2. Collections 19   3. Show 16   4. Deriving 13   5. Coinductive 12   6. Jordan_Normal_Form 12   7. Polynomial_Factorization 12   8. Regular-Sets 12   9." />
+<meta property="og:description" content="712 Entries   436 Authors   ~226,200 Lemmas   ~3,664,100 Lines of Code   Most used AFP entries:   Name Used by ? entries   1. List-Index 22   2. Collections 19   3. Show 16   4. Deriving 13   5. Coinductive 12   6. Jordan_Normal_Form 12   7. Polynomial_Factorization 12   8. Regular-Sets 12   9." />
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-<meta name="twitter:description" content="712 Entries   436 Authors   ~226,200 Lemmas   ~3,664,200 Lines of Code   Most used AFP entries:   Name Used by ? entries   1. List-Index 22   2. Collections 19   3. Show 16   4. Deriving 13   5. Coinductive 12   6. Jordan_Normal_Form 12   7. Polynomial_Factorization 12   8. Regular-Sets 12   9."/>
+<meta name="twitter:description" content="712 Entries   436 Authors   ~226,200 Lemmas   ~3,664,100 Lines of Code   Most used AFP entries:   Name Used by ? entries   1. List-Index 22   2. Collections 19   3. Show 16   4. Deriving 13   5. Coinductive 12   6. Jordan_Normal_Form 12   7. Polynomial_Factorization 12   8. Regular-Sets 12   9."/>
 
   
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     <span class='first'>S</span>tatistics</h1>
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     <td class="statsnumber">712</td>
     <td><a href="../">Entries</a></td>
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   <tr>
     <td class="statsnumber">436</td>
     <td><a href="../authors/">Authors</a></td>
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     <td class="statsnumber">~226,200</td>
     <td>Lemmas</td>
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-    <td class="statsnumber">~3,664,200</td>
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 <h4>Most used AFP entries:</h4>
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     <th>Name</th>
     <th>Used by ? entries</th>
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     <td><a href="../dependencies/list-index/">22</a></td>
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     <td>5.</td>
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     <td><a href="../dependencies/coinductive/">12</a></td>
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     <td>6.</td>
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     <td><a href="../dependencies/jordan_normal_form/">12</a></td>
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   <tr>
     <td>7.</td>
     <td><a href="../entries/Polynomial_Factorization.html">Polynomial_Factorization</a></td>
     <td><a href="../dependencies/polynomial_factorization/">12</a></td>
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   <tr>
     <td>8.</td>
     <td><a href="../entries/Regular-Sets.html">Regular-Sets</a></td>
     <td><a href="../dependencies/regular-sets/">12</a></td>
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     <td>9.</td>
     <td><a href="../entries/Landau_Symbols.html">Landau_Symbols</a></td>
     <td><a href="../dependencies/landau_symbols/">11</a></td>
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   <tr>
     <td>10.</td>
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     <td><a href="../dependencies/abstract-rewriting/">10</a></td>
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   <tr>
     <td>11.</td>
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     <td><a href="../dependencies/automatic_refinement/">10</a></td>
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   <tr>
     <td>12.</td>
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     <td><a href="../dependencies/native_word/">10</a></td>
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us','Card_Equiv_Relations','Posix-Lexing','Tree_Decomposition','Word_Lib','Noninterference_Concurrent_Composition','Algebraic_VCs','Catalan_Numbers','Dependent_SIFUM_Type_Systems','Card_Multisets','Category3','Dependent_SIFUM_Refinement','IP_Addresses','Resolution_FOL','Rewriting_Z','Buildings','DFS_Framework','Pairing_Heap','Surprise_Paradox','Ptolemys_Theorem','Refine_Imperative_HOL','EdmondsKarp_Maxflow','InfPathElimination','Simple_Firewall','Routing','Stirling_Formula','Stone_Algebras','SuperCalc','Iptables_Semantics','Lambda_Free_RPOs','Allen_Calculus','Fisher_Yates','Lp','Chord_Segments','Berlekamp_Zassenhaus','SPARCv8','Source_Coding_Theorem','LOFT','Stable_Matching','Modal_Logics_for_NTS','Deep_Learning','Lambda_Free_KBOs','Nested_Multisets_Ordinals','Separata','Abs_Int_ITP2012','Complx','Paraconsistency','Proof_Strategy_Language','Twelvefold_Way','Concurrent_Ref_Alg','FOL_Harrison','Password_Authentication_Protocol','UPF_Firewall','E_Transcendental','Bertrands_Postulate','Minimal_SSA','Bernoulli','Key_Agreement_Strong_Adversaries','Stone_Relation_Algebras','Abstract_Soundness','Differential_Dynamic_Logic','Menger','Elliptic_Curves_Group_Law','Euler_MacLaurin','Comparison_Sort_Lower_Bound','Quick_Sort_Cost','Random_BSTs','Subresultants','Lazy_Case','Constructor_Funs','LocalLexing','Types_Tableaus_and_Goedels_God','MonoidalCategory','CryptHOL','Game_Based_Crypto','Monad_Normalisation','Monomorphic_Monad','Probabilistic_While','Floyd_Warshall','Dict_Construction','Security_Protocol_Refinement','Optics','Flow_Networks','Prpu_Maxflow','Buffons_Needle','PSemigroupsConvolution','Propositional_Proof_Systems','Stone_Kleene_Relation_Algebras','CRDT','Name_Carrying_Type_Inference','Minkowskis_Theorem','HOLCF-Prelude','Decl_Sem_Fun_PL','DynamicArchitectures','Stewart_Apollonius','LambdaMu','Orbit_Stabiliser','Root_Balanced_Tree','First_Welfare_Theorem','AnselmGod','PLM','Lowe_Ontological_Argument','Dirichlet_Series','Linear_Recurrences','Zeta_Function','Diophantine_Eqns_Lin_Hom','Count_Complex_Roots','Winding_Number_Eval','Buchi_Complementation','Transition_Systems_and_Automata','Kuratowski_Closure_Complement','Hybrid_Multi_Lane_Spatial_Logic','IMAP-CRDT','Stochastic_Matrices','Knuth_Morris_Pratt','BNF_Operations','Dirichlet_L','Mason_Stothers','Median_Of_Medians_Selection','Falling_Factorial_Sum','Taylor_Models','Green','Gromov_Hyperbolicity','Ordered_Resolution_Prover','LLL_Basis_Reduction','Error_Function','First_Order_Terms','LLL_Factorization','Treaps','Hoare_Time','Architectural_Design_Patterns','CakeML','Weight_Balanced_Trees','Fishburn_Impossibility','BNF_CC','VerifyThis2018','WebAssembly','Modular_Assembly_Kit_Security','OpSets','Monad_Memo_DP','AxiomaticCategoryTheory','Irrationality_J_Hancl','Probabilistic_Timed_Automata','Hidden_Markov_Models','Optimal_BST','Partial_Order_Reduction','Localization_Ring','Projective_Geometry','Pell','Neumann_Morgenstern_Utility','DiscretePricing','Minsky_Machines','Simplex','Budan_Fourier','Quaternions','Octonions','Aggregation_Algebras','Prime_Number_Theorem','Signature_Groebner','Symmetric_Polynomials','Pi_Transcendental','Factored_Transition_System_Bounding','Lambda_Free_EPO','Randomised_BSTs','Smooth_Manifolds','Epistemic_Logic','GewirthPGCProof','Generic_Deriving','Matroids','Auto2_HOL','Functional_Ordered_Resolution_Prover','Graph_Saturation','Order_Lattice_Props','Quantales','Transformer_Semantics','Constructive_Cryptography','Auto2_Imperative_HOL','Concurrent_Revisions','Core_DOM','Store_Buffer_Reduction','Higher_Order_Terms','IMP2','Farkas','List_Inversions','UTP','Universal_Turing_Machine','Probabilistic_Prime_Tests','Kruskal','Prime_Distribution_Elementary','Safe_OCL','QHLProver','Transcendence_Series_Hancl_Rucki','Binding_Syntax_Theory','LTL_Master_Theorem','HOL-CSP','Multi_Party_Computation','LambdaAuth','KD_Tree','Differential_Game_Logic','IMP2_Binary_Heap','Groebner_Macaulay','Nullstellensatz','Linear_Inequalities','Prim_Dijkstra_Simple','Priority_Search_Trees','Complete_Non_Orders','MFOTL_Monitor','CakeML_Codegen','FOL_Seq_Calc1','Szpilrajn','TESL_Language','Stellar_Quorums','IMO2019','C2KA_DistributedSystems','Linear_Programming','Laplace_Transform','Adaptive_State_Counting','Jacobson_Basic_Algebra','Fourier','Hybrid_Systems_VCs','Generic_Join','Clean','Sigma_Commit_Crypto','Aristotles_Assertoric_Syllogistic','VerifyThis2019','Isabelle_C','ZFC_in_HOL','Interval_Arithmetic_Word32','Generalized_Counting_Sort','Gauss_Sums','Complex_Geometry','Poincare_Disc','Poincare_Bendixson','Hybrid_Logic','Zeta_3_Irrational','Bicategory','Skip_Lists','Closest_Pair_Points','Approximation_Algorithms','Mersenne_Primes','Subset_Boolean_Algebras','Arith_Prog_Rel_Primes','VeriComp','Goodstein_Lambda','Hello_World','Relational-Incorrectness-Logic','Furstenberg_Topology','WOOT_Strong_Eventual_Consistency','Lucas_Theorem','Automated_Stateful_Protocol_Verification','Stateful_Protocol_Composition_and_Typing','MFODL_Monitor_Optimized','Saturation_Framework','Sliding_Window_Algorithm','ADS_Functor','Matrices_for_ODEs','Gaussian_Integers','Lambert_W','Power_Sum_Polynomials','Attack_Trees','Banach_Steinhaus','Forcing','LTL_Normal_Form','Recursion-Addition','Irrational_Series_Erdos_Straus','Knuth_Bendix_Order','Nash_Williams','Smith_Normal_Form','Safe_Distance','Relational_Paths','Chandy_Lamport','Ordinal_Partitions','Amicable_Numbers','BirdKMP','Saturation_Framework_Extensions','Relational_Disjoint_Set_Forests','Inductive_Inference','PAC_Checker','Extended_Finite_State_Machine_Inference','Extended_Finite_State_Machines','Goedel_HFSet_Semantic','Goedel_HFSet_Semanticless','Goedel_Incompleteness','Robinson_Arithmetic','Syntax_Independent_Logic','Core_SC_DOM','DOM_Components','SC_DOM_Components','Shadow_DOM','Shadow_SC_DOM','Finite-Map-Extras','Physical_Quantities','AI_Planning_Languages_Semantics','Verified_SAT_Based_AI_Planning','CSP_RefTK','Isabelle_Marries_Dirac','Relational_Method','Interpreter_Optimizations','Relational_Minimum_Spanning_Trees','Topological_Semantics','Delta_System_Lemma','JinjaDCI','Hood_Melville_Queue','Blue_Eyes','IsaGeoCoq','Laws_of_Large_Numbers','Formal_Puiseux_Series','BTree','Sunflowers','Mereology','Hermite_Lindemann','Projective_Measurements','Modular_arithmetic_LLL_and_HNF_algorithms','Constructive_Cryptography_CM','Padic_Ints','Grothendieck_Schemes','IFC_Tracking','Progress_Tracking','GaleStewart_Games','BenOr_Kozen_Reif','Lifting_the_Exponent','Metalogic_ProofChecker','Regression_Test_Selection','Combinatorics_Words','Combinatorics_Words_Graph_Lemma','Combinatorics_Words_Lyndon','IMP_Compiler','Public_Announcement_Logic','MiniSail','Van_der_Waerden','SpecCheck','Finitely_Generated_Abelian_Groups','Schutz_Spacetime','Relational_Forests','Design_Theory','BD_Security_Compositional','CoCon','CoSMeDis','CoSMed','Fresh_Identifiers','Three_Circles','Logging_Independent_Anonymity','Cubic_Quartic_Equations','Dominance_CHK','CZH_Elementary_Categories','CZH_Foundations','CZH_Universal_Constructions','Conditional_Simplification','Conditional_Transfer_Rule','Intro_Dest_Elim','Types_To_Sets_Extension','Weighted_Path_Order','Complex_Bounded_Operators','FOL_Axiomatic','Virtual_Substitution','Correctness_Algebras','X86_Semantics','Belief_Revision','Registers','Szemeredi_Regularity','Factor_Algebraic_Polynomial','PAL','Real_Power','SimplifiedOntologicalArgument','Hahn_Jordan_Decomposition','Foundation_of_geometry','Van_Emde_Boas_Trees','Simplicial_complexes_and_boolean_functions','Regular_Tree_Relations','MDP-Algorithms','MDP-Rewards','Roth_Arithmetic_Progressions','Gale_Shapley','Hyperdual','Knights_Tour','Irrationals_From_THEBOOK','Actuarial_Mathematics','Median_Method','Interpolation_Polynomials_HOL_Algebra','FOL_Seq_Calc2','Youngs_Inequality','FO_Theory_Rewriting','LP_Duality','Quasi_Borel_Spaces','Equivalence_Relation_Enumeration','VYDRA_MDL','Eval_FO','Wetzels_Problem','Universal_Hash_Families','ResiduatedTransitionSystem','Transitive_Models','Independence_CH','Cotangent_PFD_Formula','FOL_Seq_Calc3','Ackermanns_not_PR','Dedekind_Real','Frequency_Moments','Prefix_Free_Code_Combinators','Sophomores_Dream','Digit_Expansions','Multiset_Ordering_NPC','Fishers_Inequality','Clique_and_Monotone_Circuits','Package_logic','Pluennecke_Ruzsa_Inequality','Combinable_Wands','Rewrite_Properties_Reduction','DPRM_Theorem','Finite_Fields','IsaNet','Boolos_Curious_Inference','Real_Time_Deque','IMP_Compiler_Reuse','Weighted_Arithmetic_Geometric_Mean','Commuting_Hermitian','Solidity','Nano_JSON','FSM_Tests','Involutions2Squares','SCC_Bloemen_Sequential','Number_Theoretic_Transform','Hales_Jewett','Khovanskii_Theorem','Separation_Logic_Unbounded','CRYSTALS-Kyber','Implicational_Logic','Risk_Free_Lending','Padic_Field','Stalnaker_Logic','Safe_Range_RC','Maximum_Segment_Sum','Undirected_Graph_Theory','Query_Optimization','PAPP_Impossibility','Balog_Szemeredi_Gowers','Combinatorial_Enumeration_Algorithms']
   const article_years_unique = ['2004','','','','','','','','','','','','','','2005','','','','','','','','2006','','','','','','','2007','','','','','','','','2008','','','','','','','','','','','','','','','2009','','','','','','','','','','','','2010','','','','','','','','','','','','','','','','','','','','','','2011','','','','','','','','','','','','','','','','','2012','','','','','','','','','','','','','','','','','','','','','','','','','2013','','','','','','','','','','','','','','','','','','','','','','','2014','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','2015','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','2016','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','2017','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','2018','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','2019','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','2020','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','2021','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','2022','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','','']
-  const loc_articles = [839,1507,1542,1096,1058,2419,44195,205,142,1974,209,1110,3792,506,1141,3766,17615,3119,6430,1145,447,2537,1275,1583,1838,12832,13047,2685,1228,3556,4238,9647,2847,970,1740,79712,4738,3396,2185,10664,31022,6726,30332,180,793,1047,14413,2080,254,2221,5959,3463,799,1540,684,6654,8,2627,27490,264,32555,5025,4380,208,9533,447,2380,3399,606,6305,2060,840,713,1024,5632,1427,4078,2230,6003,22604,1602,3370,1587,2451,2591,260,1617,16,2937,6557,7804,6381,992,125,10130,332,239,1831,999,1756,4420,434,4461,11864,2835,8575,1045,408,2940,2613,37935,3243,1480,2612,3141,2580,23005,27588,2266,4107,7701,1249,260,5309,73,9729,719,6674,1512,4355,1249,1908,6214,4977,10086,7261,538,3830,4591,202,853,1784,5274,10304,1524,150,5292,706,2248,10737,1463,1958,3067,11487,1860,1190,1219,2174,1144,14860,2212,1957,166,10685,6419,572,590,465,1698,1909,4134,1403,2138,2280,1959,2467,220,4432,9396,5430,3999,4472,406,5935,1829,12828,3234,9486,4560,926,659,63,1653,2338,9085,753,2113,875,2563,627,945,1405,1296,7880,1922,90,28055,2879,2796,1116,5259,4863,8842,1356,5986,527,6658,2606,1772,5327,1092,4112,952,1064,2362,1089,2446,477,2074,3763,1954,710,16080,8267,908,1063,21228,9679,8661,3142,9156,695,435,13995,478,898,10416,2724,1162,741,405,495,498,838,3622,4616,6264,4106,8166,12091,3178,518,17581,2876,2418,5496,885,2453,1162,17387,509,703,5047,10687,4287,3811,5337,329,3985,1057,15080,3257,2582,553,8478,206,26817,8773,3324,2960,398,12811,9483,370,173,384,18990,2545,6119,3774,645,2415,4344,9370,20053,3963,3419,319,3174,169,19414,14667,541,2652,7059,7590,3898,3243,4507,855,2289,5027,1349,276,4339,1475,3482,7119,9662,601,1728,852,2194,12204,4212,590,13558,1695,4484,1644,694,835,737,3394,105,68,10492,1127,8501,11278,4135,378,4711,1200,2078,639,14059,3160,3930,4869,468,1531,5570,5683,1993,4205,478,4121,3146,3472,88,480,1261,1877,2193,250,10669,822,7466,3105,5302,2782,8208,8809,2324,6164,945,6514,992,489,810,8949,3434,338,854,493,4593,9457,15962,6402,10342,787,2288,3259,1820,8442,3278,12945,672,843,3402,3638,11570,13548,3734,6261,528,965,7711,1042,1221,5017,1390,2755,1622,2173,13357,805,10042,2667,541,1271,2668,5319,9770,2765,934,11918,2205,1743,7917,1209,449,685,1812,1227,3559,3578,2951,2218,1644,5182,4968,2767,17368,34354,3204,6019,1900,373,9969,30917,3018,3298,5306,4576,10509,986,15793,4437,9487,5543,3301,1264,2973,805,10229,2606,5735,3365,472,3604,3199,13289,987,787,4455,527,713,782,2335,2134,9936,2090,3736,5801,2350,4124,3809,176,1726,9701,7027,5069,5729,4562,14098,10292,6402,4470,1907,68336,2355,3937,3485,1706,3154,944,1033,597,370,691,764,2564,332,21109,23314,10943,3061,744,2353,1560,2537,1609,1239,1939,1338,12002,1034,1444,1902,2670,755,13319,3036,5074,9793,6287,1261,2908,2101,5117,12873,9018,4265,4731,426,11477,3546,1295,8100,16384,3523,7793,12668,15385,648,1761,2352,16434,2359,7700,3995,6542,4731,2826,3304,24539,745,365,26525,290,2582,15792,615,4039,3766,4959,17068,8442,15847,6578,4131,7218,1015,10339,384,9264,4094,13798,488,837,666,840,19737,1088,233,4433,7684,1962,4940,3003,11165,14638,5913,303,3758,817,1329,3157,40867,29106,22137,225,1053,176,17526,4239,17781,1306,21773,13533,2621,1324,5953,909,2961,133,2203,455,2619,6076,20665,1882,9541,4288,4298,1384,2007,2946,3108,269,948,566,757,2594,807,9208,624,8738,502,7222,5937,342,828,18280,18383,14310,730,719,200,1411,4182,816,401,1312,1820,5168,2337,2169,654,2031,3338,8759,4623,7346,95,3711,1527,414,5785,15325,1041,53757,351,3175,1958,2144,1388,2325,3584,431,1923,39761,534,3097,144,2696,19120,2421,2961,1593]
+  const loc_articles = [839,1507,1542,1096,1058,2419,44195,205,142,1974,209,1110,3792,506,1141,3766,17615,3119,6430,1145,447,2537,1275,1583,1838,12832,13047,2685,1228,3556,4238,9647,2847,970,1740,79712,4738,3396,2185,10664,31022,6726,30332,180,793,1047,14413,2080,254,2221,5959,3463,799,1540,684,6654,8,2627,27490,264,32555,5025,4380,208,9533,447,2380,3399,606,6305,2060,840,713,1024,5632,1427,4078,2230,6003,22604,1602,3370,1587,2451,2591,260,1617,16,2937,6557,7804,6381,992,125,10130,332,239,1831,999,1756,4420,434,4461,11864,2835,8575,1045,408,2940,2613,37935,3243,1480,2612,3141,2580,23005,27588,2266,4107,7701,1249,260,5309,73,9729,719,6674,1512,4355,1249,1908,6214,4977,10086,7261,538,3830,4591,202,853,1784,5274,10304,1524,150,5292,706,2248,10737,1463,1958,3067,11487,1860,1190,1219,2174,1144,14860,2212,1957,166,10685,6419,572,590,465,1698,1909,4134,1403,2138,2280,1959,2467,220,4432,9396,5430,3999,4472,406,5935,1829,12828,3234,9486,4560,926,659,63,1653,2338,9085,753,2113,875,2563,627,945,1405,1296,7880,1922,90,28055,2879,2796,1116,5259,4863,8842,1356,5986,527,6658,2606,1772,5327,1092,4112,952,1064,2362,1089,2446,477,2074,3763,1954,710,16080,8267,908,1063,21228,9679,8661,3142,9156,695,435,13995,478,898,10416,2724,1162,741,405,495,498,838,3622,4616,6264,4106,8166,12091,3178,518,17581,2876,2418,5496,885,2453,1162,17387,509,703,5047,10687,4287,3811,5337,329,3985,1057,15080,3257,2582,553,8478,206,26817,8773,3324,2960,398,12811,9483,370,173,384,18990,2545,6119,3774,645,2415,4344,9370,20053,3963,3419,319,3174,169,19414,14667,541,2652,7059,7590,3898,3243,4507,855,2289,5027,1349,276,4339,1475,3482,7119,9662,601,1728,852,2194,12204,4212,590,13558,1695,4484,1644,694,835,737,3394,105,68,10492,1127,8501,11278,4135,378,4711,1200,2078,639,14059,3160,3930,4869,468,1531,5570,5683,1993,4205,478,4121,3146,3472,88,480,1261,1877,2193,250,10669,822,7466,3105,5302,2782,8208,8809,2324,6164,945,6514,992,489,810,8949,3434,338,854,493,4593,9457,15962,6402,10342,787,2288,3259,1820,8442,3278,12945,672,843,3402,3638,11570,13548,3734,6261,528,965,7711,1042,1221,5017,1390,2755,1622,2173,13357,805,10042,2667,541,1271,2668,5319,9770,2765,934,11918,2205,1743,7917,1209,449,685,1812,1227,3559,3578,2951,2218,1644,5182,4968,2767,17368,34354,3204,6019,1900,373,9969,30917,3018,3298,5306,4576,10509,986,15793,4437,9487,5543,3301,1264,2973,805,10229,2606,5735,3365,472,3604,3199,13289,987,787,4455,527,713,782,2335,2134,9936,2090,3736,5801,2350,4124,3809,176,1726,9701,7027,5069,5729,4562,14098,10292,6402,4470,1907,68336,2355,3937,3485,1706,3154,944,1033,597,370,691,764,2564,332,21109,23314,10943,3061,744,2353,1560,2537,1609,1239,1939,1338,12002,1034,1444,1902,2670,755,13319,3036,5074,9793,6287,1261,2908,2101,5117,12873,9018,4265,4731,426,11477,3546,1295,8100,16384,3523,7793,12668,15385,648,1761,2352,16434,2359,7700,3995,6542,4731,2826,3304,24539,745,365,26525,290,2582,15792,615,4039,3766,4959,17068,8442,15847,6578,4131,7218,1015,10339,384,9264,4094,13798,488,837,666,840,19737,1088,233,4433,7684,1962,4940,3003,11165,14638,5913,303,3758,817,1329,3157,40867,29106,22137,225,1053,176,17526,4239,17781,1306,21773,13533,2621,1324,5953,909,2961,133,2203,455,2619,6076,20665,1882,9541,4288,4298,1384,2007,2946,3108,269,948,566,757,2594,807,9208,624,8738,502,7222,5937,342,828,18280,18383,14310,730,719,200,1411,4182,816,401,1312,1820,5168,2337,2169,654,2031,3338,8759,4623,7346,95,3711,1527,414,5785,15325,1041,53757,351,3175,1958,2144,1388,2325,3584,431,1923,39761,534,3097,144,2696,19120,2366,2961,1593]
 </script>
 <h4>Growth in number of entries:</h4>
 <script src="../js/Chart.js"></script>
 <div class="chart">
   <canvas id="num-articles-canvas"></canvas>
 </div>
 <script>
   new Chart(document.getElementById("num-articles-canvas"), {
     type: 'bar',
     data: {
       labels: years,
       datasets: [{
         label: 'Size of the AFP in # of entries',
         data: no_articles,
         backgroundColor: "rgba(46, 45, 78, 1)"
       }],
     },
     options: {
       responsive: true,
       maintainAspectRatio: false,
       scales: {
         yAxes: [{
           ticks: {
             beginAtZero: true
           }
         }]
       },
     }
   })
 </script>
 
 <h4>Growth in lines of code:</h4>
 <div class="chart">
   <canvas id="loc-years-canvas"></canvas>
 </div>
 <script>
   new Chart(document.getElementById("loc-years-canvas"), {
     type: 'bar',
     data: {
       labels: years,
       datasets: [{
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       scales: {
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             beginAtZero: true
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       },
     }
   })
 </script>
 
 <h4>Growth in number of authors:</h4>
 <div class="chart">
   <canvas id="author-years-canvas"></canvas>
 </div>
 <script>
   new Chart(document.getElementById("author-years-canvas"), {
     type: 'bar',
     data: {
       labels: years,
       datasets: [{
         label: 'new authors per year',
         data: no_authors,
         backgroundColor: "rgba(101, 99, 136, 1)"
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         label: 'number of authors contributing (cumulative)',
         data: no_authors_series,
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       scales: {
         yAxes: [{
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       },
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   })
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 <h4>Size of entries:</h4>
 <div class="chart">
   <canvas id="loc-articles-canvas"></canvas>
 </div>
 <script>
   new Chart(document.getElementById("loc-articles-canvas"), {
     type: 'bar',
     data: {
       labels: article_years_unique,
       datasets: [{
         label: 'loc per article',
         data: loc_articles,
         backgroundColor: 'rgba(101, 99, 136, 1)'
       }]
     },
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       responsive: true,
       maintainAspectRatio: false,
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         yAxes: [{
           ticks: {
             beginAtZero: true
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         }]
       },
       tooltips: {
         callbacks: {
           title: tooltipItem => all_articles[tooltipItem[0].index]
         }
       }
     }
   })
 </script>
 
 </td>
 </tr>
 
 </tbody>
 </table>
 
 </div>
     </div>
   </div>
 </body>
 
 </html>
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