diff --git a/src/HOL/Analysis/Metric_Arith.thy b/src/HOL/Analysis/Metric_Arith.thy
--- a/src/HOL/Analysis/Metric_Arith.thy
+++ b/src/HOL/Analysis/Metric_Arith.thy
@@ -1,112 +1,112 @@
 (*  Title:    Metric_Arith.thy
     Author:   Maximilian Schäffeler (port from HOL Light)
 *)
 
 section \<open>A decision procedure for metric spaces\<close>
 
 theory Metric_Arith
   imports HOL.Real_Vector_Spaces
 begin
 
 text \<open>
 A port of the decision procedure ``Formalization of metric spaces in HOL Light''
 @{cite "DBLP:journals/jar/Maggesi18"} for the type class @{class metric_space},
 with the \<open>Argo\<close> solver as backend.
 \<close>
 
 named_theorems metric_prenex
 named_theorems metric_nnf
 named_theorems metric_unfold
 named_theorems metric_pre_arith
 
 lemmas pre_arith_simps =
   max.bounded_iff max_less_iff_conj
   le_max_iff_disj less_max_iff_disj
   simp_thms HOL.eq_commute
 declare pre_arith_simps [metric_pre_arith]
 
 lemmas unfold_simps =
   Un_iff subset_iff disjoint_iff_not_equal
   Ball_def Bex_def
 declare unfold_simps [metric_unfold]
 
 declare HOL.nnf_simps(4) [metric_prenex]
 
 lemma imp_prenex [metric_prenex]:
   "\<And>P Q. (\<exists>x. P x) \<longrightarrow> Q \<equiv> \<forall>x. (P x \<longrightarrow> Q)"
   "\<And>P Q. P \<longrightarrow> (\<exists>x. Q x) \<equiv> \<exists>x. (P \<longrightarrow> Q x)"
   "\<And>P Q. (\<forall>x. P x) \<longrightarrow> Q \<equiv> \<exists>x. (P x \<longrightarrow> Q)"
   "\<And>P Q. P \<longrightarrow> (\<forall>x. Q x) \<equiv> \<forall>x. (P \<longrightarrow> Q x)"
   by simp_all
 
 lemma ex_prenex [metric_prenex]:
   "\<And>P Q. (\<exists>x. P x) \<and> Q \<equiv> \<exists>x. (P x \<and> Q)"
   "\<And>P Q. P \<and> (\<exists>x. Q x) \<equiv> \<exists>x. (P \<and> Q x)"
   "\<And>P Q. (\<exists>x. P x) \<or> Q \<equiv> \<exists>x. (P x \<or> Q)"
   "\<And>P Q. P \<or> (\<exists>x. Q x) \<equiv> \<exists>x. (P \<or> Q x)"
   "\<And>P. \<not>(\<exists>x. P x) \<equiv> \<forall>x. \<not>P x"
   by simp_all
 
 lemma all_prenex [metric_prenex]:
   "\<And>P Q. (\<forall>x. P x) \<and> Q \<equiv> \<forall>x. (P x \<and> Q)"
   "\<And>P Q. P \<and> (\<forall>x. Q x) \<equiv> \<forall>x. (P \<and> Q x)"
   "\<And>P Q. (\<forall>x. P x) \<or> Q \<equiv> \<forall>x. (P x \<or> Q)"
   "\<And>P Q. P \<or> (\<forall>x. Q x) \<equiv> \<forall>x. (P \<or> Q x)"
   "\<And>P. \<not>(\<forall>x. P x) \<equiv> \<exists>x. \<not>P x"
   by simp_all
 
 lemma nnf_thms [metric_nnf]:
   "(\<not> (P \<and> Q)) = (\<not> P \<or> \<not> Q)"
   "(\<not> (P \<or> Q)) = (\<not> P \<and> \<not> Q)"
   "(P \<longrightarrow> Q) = (\<not> P \<or> Q)"
   "(P = Q) \<longleftrightarrow> (P \<or> \<not> Q) \<and> (\<not> P \<or> Q)"
   "(\<not> (P = Q)) \<longleftrightarrow> (\<not> P \<or> \<not> Q) \<and> (P \<or> Q)"
   "(\<not> \<not> P) = P"
   by blast+
 
 lemmas nnf_simps = nnf_thms linorder_not_less linorder_not_le
 declare nnf_simps[metric_nnf]
 
 lemma ball_insert: "(\<forall>x\<in>insert a B. P x) = (P a \<and> (\<forall>x\<in>B. P x))"
   by blast
 
 lemma Sup_insert_insert:
   fixes a::real
   shows "Sup (insert a (insert b s)) = Sup (insert (max a b) s)"
   by (simp add: Sup_real_def)
 
 lemma real_abs_dist: "\<bar>dist x y\<bar> = dist x y"
   by simp
 
 lemma maxdist_thm [THEN HOL.eq_reflection]:
   assumes "finite s" "x \<in> s" "y \<in> s"
   defines "\<And>a. f a \<equiv> \<bar>dist x a - dist a y\<bar>"
   shows "dist x y = Sup (f ` s)"
 proof -
   have "dist x y \<le> Sup (f ` s)"
   proof -
     have "finite (f ` s)"
       by (simp add: \<open>finite s\<close>)
     moreover have "\<bar>dist x y - dist y y\<bar> \<in> f ` s"
       by (metis \<open>y \<in> s\<close> f_def imageI)
     ultimately show ?thesis
       using le_cSup_finite by simp
   qed
   also have "Sup (f ` s) \<le> dist x y"
     using \<open>x \<in> s\<close> cSUP_least[of s f] abs_dist_diff_le
     unfolding f_def
     by blast
   finally show ?thesis .
 qed
 
 theorem metric_eq_thm [THEN HOL.eq_reflection]:
   "x \<in> s \<Longrightarrow> y \<in> s \<Longrightarrow> x = y \<longleftrightarrow> (\<forall>a\<in>s. dist x a = dist y a)"
   by auto
 
-ML_file "metricarith.ml"
+ML_file "metric_arith.ML"
 
 method_setup metric = \<open>
   Scan.succeed (SIMPLE_METHOD' o MetricArith.metric_arith_tac)
 \<close> "prove simple linear statements in metric spaces (\<forall>\<exists>\<^sub>p fragment)"
 
 end
\ No newline at end of file
diff --git a/src/HOL/Analysis/metricarith.ml b/src/HOL/Analysis/metric_arith.ML
rename from src/HOL/Analysis/metricarith.ml
rename to src/HOL/Analysis/metric_arith.ML