diff --git a/src/HOL/Tools/SMT/smt_translate.ML b/src/HOL/Tools/SMT/smt_translate.ML
--- a/src/HOL/Tools/SMT/smt_translate.ML
+++ b/src/HOL/Tools/SMT/smt_translate.ML
@@ -1,540 +1,540 @@
 (*  Title:      HOL/Tools/SMT/smt_translate.ML
     Author:     Sascha Boehme, TU Muenchen
 
 Translate theorems into an SMT intermediate format and serialize them.
 *)
 
 signature SMT_TRANSLATE =
 sig
   (*intermediate term structure*)
   datatype squant = SForall | SExists
   datatype 'a spattern = SPat of 'a list | SNoPat of 'a list
   datatype sterm =
     SVar of int * sterm list |
     SConst of string * sterm list |
     SQua of squant * string list * sterm spattern list * sterm
 
   (*translation configuration*)
   type sign = {
     logic: string,
     sorts: string list,
     dtyps: (BNF_Util.fp_kind * (string * (string * (string * string) list) list)) list,
     funcs: (string * (string list * string)) list }
   type config = {
     order: SMT_Util.order,
     logic: string -> term list -> string,
     fp_kinds: BNF_Util.fp_kind list,
     serialize: (string * string) list -> string list -> sign -> (SMT_Util.role * sterm) list ->
       string }
   type replay_data = {
     context: Proof.context,
     typs: typ Symtab.table,
     terms: term Symtab.table,
     ll_defs: term list,
     rewrite_rules: thm list,
     assms: ((int * SMT_Util.role) * thm) list }
 
   (*translation*)
   val add_config: SMT_Util.class * (Proof.context -> config) -> Context.generic -> Context.generic
   val translate: Proof.context -> string -> (string * string) list -> string list ->
     ((int * SMT_Util.role) * thm) list ->
     string * replay_data
 end;
 
 structure SMT_Translate: SMT_TRANSLATE =
 struct
 
 
 (* intermediate term structure *)
 
 datatype squant = SForall | SExists
 
 datatype 'a spattern =
   SPat of 'a list | SNoPat of 'a list
 
 datatype sterm =
   SVar of int * sterm list |
   SConst of string * sterm list |
   SQua of squant * string list * sterm spattern list * sterm
 
 
 (* translation configuration *)
 
 type sign = {
   logic: string,
   sorts: string list,
   dtyps: (BNF_Util.fp_kind * (string * (string * (string * string) list) list)) list,
   funcs: (string * (string list * string)) list }
 
 type config = {
   order: SMT_Util.order,
   logic: string -> term list -> string,
   fp_kinds: BNF_Util.fp_kind list,
   serialize: (string * string) list -> string list -> sign -> (SMT_Util.role * sterm) list ->
     string }
 
 type replay_data = {
   context: Proof.context,
   typs: typ Symtab.table,
   terms: term Symtab.table,
   ll_defs: term list,
   rewrite_rules: thm list,
   assms: ((int * SMT_Util.role) * thm) list }
 
 
 (* translation context *)
 
 fun add_components_of_typ (Type (s, Ts)) =
     cons (Long_Name.base_name s) #> fold_rev add_components_of_typ Ts
   | add_components_of_typ (TFree (s, _)) = cons (perhaps (try (unprefix "'")) s)
   | add_components_of_typ _ = I;
 
 fun suggested_name_of_typ T = space_implode "_" (add_components_of_typ T []);
 
 fun suggested_name_of_term (Const (s, _)) = Long_Name.base_name s
   | suggested_name_of_term (Free (s, _)) = s
   | suggested_name_of_term _ = Name.uu
 
 val empty_tr_context = (Name.context, Typtab.empty, Termtab.empty)
 val safe_suffix = "$"
 
 fun add_typ T proper (cx as (names, typs, terms)) =
   (case Typtab.lookup typs T of
     SOME (name, _) => (name, cx)
   | NONE =>
       let
         val sugg = Name.desymbolize (SOME true) (suggested_name_of_typ T) ^ safe_suffix
         val (name, names') = Name.variant sugg names
         val typs' = Typtab.update (T, (name, proper)) typs
       in (name, (names', typs', terms)) end)
 
 fun add_fun t sort (cx as (names, typs, terms)) =
   (case Termtab.lookup terms t of
     SOME (name, _) => (name, cx)
   | NONE =>
       let
         val sugg = Name.desymbolize (SOME false) (suggested_name_of_term t) ^ safe_suffix
         val (name, names') = Name.variant sugg names
         val terms' = Termtab.update (t, (name, sort)) terms
       in (name, (names', typs, terms')) end)
 
 fun sign_of logic dtyps (_, typs, terms) = {
   logic = logic,
   sorts = Typtab.fold (fn (_, (n, true)) => cons n | _ => I) typs [],
   dtyps = dtyps,
   funcs = Termtab.fold (fn (_, (n, SOME ss)) => cons (n,ss) | _ => I) terms []}
 
 fun replay_data_of ctxt ll_defs rules assms (_, typs, terms) =
   let
     fun add_typ (T, (n, _)) = Symtab.update (n, T)
     val typs' = Typtab.fold add_typ typs Symtab.empty
 
     fun add_fun (t, (n, _)) = Symtab.update (n, t)
     val terms' = Termtab.fold add_fun terms Symtab.empty
   in
     {context = ctxt, typs = typs', terms = terms', ll_defs = ll_defs, rewrite_rules = rules,
      assms = assms}
   end
 
 
 (* preprocessing *)
 
 (** (co)datatype declarations **)
 
 fun collect_co_datatypes fp_kinds (tr_context, ctxt) ts =
   let
     val (fp_decls, ctxt') =
       ([], ctxt)
       |> fold (Term.fold_types (SMT_Datatypes.add_decls fp_kinds) o snd) ts
       |>> flat
 
     fun is_decl_typ T = exists (equal T o fst o snd) fp_decls
 
     fun add_typ' T proper =
       (case SMT_Builtin.dest_builtin_typ ctxt' T of
         SOME (n, Ts) => pair n (* FIXME HO: Consider Ts *)
       | NONE => add_typ T proper)
 
     fun tr_select sel =
       let val T = Term.range_type (Term.fastype_of sel)
       in add_fun sel NONE ##>> add_typ' T (not (is_decl_typ T)) end
     fun tr_constr (constr, selects) =
       add_fun constr NONE ##>> fold_map tr_select selects
     fun tr_typ (fp, (T, cases)) =
       add_typ' T false ##>> fold_map tr_constr cases #>> pair fp
 
     val (fp_decls', tr_context') = fold_map tr_typ fp_decls tr_context
 
     fun add (constr, selects) =
       Termtab.update (constr, length selects) #>
       fold (Termtab.update o rpair 1) selects
 
     val funcs = fold (fold add o snd o snd) fp_decls Termtab.empty
 
   in ((funcs, fp_decls', tr_context', ctxt'), ts) end
     (* FIXME: also return necessary (co)datatype theorems *)
 
 
 (** eta-expand quantifiers, let expressions and built-ins *)
 
 local
   fun eta f T t = Abs (Name.uu, T, f (Term.incr_boundvars 1 t $ Bound 0))
 
   fun exp f T = eta f (Term.domain_type (Term.domain_type T))
 
   fun exp2 T q =
     let val U = Term.domain_type T
     in Abs (Name.uu, U, q $ eta I (Term.domain_type U) (Bound 0)) end
 
   fun expf k i T t =
     let val Ts = drop i (fst (SMT_Util.dest_funT k T))
     in
       Term.incr_boundvars (length Ts) t
       |> fold_rev (fn i => fn u => u $ Bound i) (0 upto length Ts - 1)
       |> fold_rev (fn T => fn u => Abs (Name.uu, T, u)) Ts
     end
 in
 
 fun eta_expand ctxt funcs =
   let
     fun exp_func t T ts =
       (case Termtab.lookup funcs t of
         SOME k => Term.list_comb (t, ts) |> k <> length ts ? expf k (length ts) T
       | NONE => Term.list_comb (t, ts))
 
     fun expand ((q as Const (\<^const_name>\<open>All\<close>, _)) $ Abs a) = q $ abs_expand a
       | expand ((q as Const (\<^const_name>\<open>All\<close>, T)) $ t) = q $ exp expand T t
       | expand (q as Const (\<^const_name>\<open>All\<close>, T)) = exp2 T q
       | expand ((q as Const (\<^const_name>\<open>Ex\<close>, _)) $ Abs a) = q $ abs_expand a
       | expand ((q as Const (\<^const_name>\<open>Ex\<close>, T)) $ t) = q $ exp expand T t
       | expand (q as Const (\<^const_name>\<open>Ex\<close>, T)) = exp2 T q
       | expand (Const (\<^const_name>\<open>Let\<close>, T) $ t) =
           let val U = Term.domain_type (Term.range_type T)
-          in Abs (Name.uu, U, Bound 0 $ Term.incr_boundvars 1 t) end
+          in Abs (Name.uu, U, expand (Bound 0 $ Term.incr_boundvars 1 t)) end
       | expand (Const (\<^const_name>\<open>Let\<close>, T)) =
           let val U = Term.domain_type (Term.range_type T)
           in Abs (Name.uu, Term.domain_type T, Abs (Name.uu, U, Bound 0 $ Bound 1)) end
       | expand t =
           (case Term.strip_comb t of
             (Const (\<^const_name>\<open>Let\<close>, _), t1 :: t2 :: ts) =>
             Term.betapplys (Term.betapply (expand t2, expand t1), map expand ts)
           | (u as Const (c as (_, T)), ts) =>
               (case SMT_Builtin.dest_builtin ctxt c ts of
                 SOME (_, k, us, mk) =>
                   if k = length us then mk (map expand us)
                   else if k < length us then chop k (map expand us) |>> mk |> Term.list_comb
                   else expf k (length ts) T (mk (map expand us))
               | NONE => exp_func u T (map expand ts))
           | (u as Free (_, T), ts) => exp_func u T (map expand ts)
           | (Abs a, ts) => Term.list_comb (abs_expand a, map expand ts)
           | (u, ts) => Term.list_comb (u, map expand ts))
 
     and abs_expand (n, T, t) = Abs (n, T, expand t)
 
   in map (apsnd expand) end
 
 end
 
 
 (** introduce explicit applications **)
 
 local
   (*
     Make application explicit for functions with varying number of arguments.
   *)
 
   fun add t i = apfst (Termtab.map_default (t, i) (Integer.min i))
   fun add_type T = apsnd (Typtab.update (T, ()))
 
   fun min_arities t =
     (case Term.strip_comb t of
       (u as Const _, ts) => add u (length ts) #> fold min_arities ts
     | (u as Free _, ts) => add u (length ts) #> fold min_arities ts
     | (Abs (_, T, u), ts) => (can dest_funT T ? add_type T) #> min_arities u #> fold min_arities ts
     | (_, ts) => fold min_arities ts)
 
   fun take_vars_into_account types t i =
     let
       fun find_min j (T as Type (\<^type_name>\<open>fun\<close>, [_, T'])) =
           if j = i orelse Typtab.defined types T then j else find_min (j + 1) T'
         | find_min j _ = j
     in find_min 0 (Term.type_of t) end
 
   fun app u (t, T) = (Const (\<^const_name>\<open>fun_app\<close>, T --> T) $ t $ u, Term.range_type T)
 
   fun apply i t T ts =
     let
       val (ts1, ts2) = chop i ts
       val (_, U) = SMT_Util.dest_funT i T
     in fst (fold app ts2 (Term.list_comb (t, ts1), U)) end
 in
 
 fun intro_explicit_application ctxt funcs ts =
   let
     val explicit_application = Config.get ctxt SMT_Config.explicit_application
     val get_arities =
       (case explicit_application of
         0 => min_arities
       | 1 => min_arities
       | 2 => K I
       | n => error ("Illegal value for " ^ quote (Config.name_of SMT_Config.explicit_application) ^
           ": " ^ string_of_int n))
 
     val (arities, types) = fold (get_arities o snd) ts (Termtab.empty, Typtab.empty)
     val arities' = arities |> explicit_application = 1 ? Termtab.map (take_vars_into_account types)
 
     fun app_func t T ts =
       if is_some (Termtab.lookup funcs t) then Term.list_comb (t, ts)
       else apply (the_default 0 (Termtab.lookup arities' t)) t T ts
 
     fun in_list T f t = SMT_Util.mk_symb_list T (map f (SMT_Util.dest_symb_list t))
 
     fun traverse Ts t =
       (case Term.strip_comb t of
         (q as Const (\<^const_name>\<open>All\<close>, _), [Abs (x, T, u)]) =>
           q $ Abs (x, T, in_trigger (T :: Ts) u)
       | (q as Const (\<^const_name>\<open>Ex\<close>, _), [Abs (x, T, u)]) =>
           q $ Abs (x, T, in_trigger (T :: Ts) u)
       | (q as Const (\<^const_name>\<open>Let\<close>, _), [u1, u2 as Abs _]) =>
           q $ traverse Ts u1 $ traverse Ts u2
       | (u as Const (c as (_, T)), ts) =>
           (case SMT_Builtin.dest_builtin ctxt c ts of
             SOME (_, k, us, mk) =>
               let
                 val (ts1, ts2) = chop k (map (traverse Ts) us)
                 val U = Term.strip_type T |>> snd o chop k |> (op --->)
               in apply 0 (mk ts1) U ts2 end
           | NONE => app_func u T (map (traverse Ts) ts))
       | (u as Free (_, T), ts) => app_func u T (map (traverse Ts) ts)
       | (u as Bound i, ts) => apply 0 u (nth Ts i) (map (traverse Ts) ts)
       | (Abs (n, T, u), ts) => traverses Ts (Abs (n, T, traverse (T::Ts) u)) ts
       | (u, ts) => traverses Ts u ts)
     and in_trigger Ts ((c as \<^Const_>\<open>trigger\<close>) $ p $ t) = c $ in_pats Ts p $ traverse Ts t
       | in_trigger Ts t = traverse Ts t
     and in_pats Ts ps =
       in_list \<^typ>\<open>pattern symb_list\<close> (in_list \<^typ>\<open>pattern\<close> (in_pat Ts)) ps
     and in_pat Ts ((p as \<^Const_>\<open>pat _\<close>) $ t) = p $ traverse Ts t
       | in_pat Ts ((p as \<^Const_>\<open>nopat _\<close>) $ t) = p $ traverse Ts t
       | in_pat _ t = raise TERM ("bad pattern", [t])
     and traverses Ts t ts = Term.list_comb (t, map (traverse Ts) ts)
   in map (apsnd (traverse [])) ts end
 
 val fun_app_eq = mk_meta_eq @{thm fun_app_def}
 
 end
 
 
 (** map HOL formulas to FOL formulas (i.e., separate formulas froms terms) **)
 
 local
   val is_quant = member (op =) [\<^const_name>\<open>All\<close>, \<^const_name>\<open>Ex\<close>]
 
   val fol_rules = [
     Let_def,
     @{lemma "P = True == P" by (rule eq_reflection) simp}]
 
   exception BAD_PATTERN of unit
 
   fun is_builtin_conn_or_pred ctxt c ts =
     is_some (SMT_Builtin.dest_builtin_conn ctxt c ts) orelse
     is_some (SMT_Builtin.dest_builtin_pred ctxt c ts)
 in
 
 fun folify ctxt =
   let
     fun in_list T f t = SMT_Util.mk_symb_list T (map_filter f (SMT_Util.dest_symb_list t))
 
     fun in_term pat t =
       (case Term.strip_comb t of
         (\<^Const_>\<open>True\<close>, []) => t
       | (\<^Const_>\<open>False\<close>, []) => t
       | (u as \<^Const_>\<open>If _\<close>, [t1, t2, t3]) =>
           if pat then raise BAD_PATTERN () else u $ in_form t1 $ in_term pat t2 $ in_term pat t3
       | (Const (c as (n, _)), ts) =>
           if is_builtin_conn_or_pred ctxt c ts orelse is_quant n then
             if pat then raise BAD_PATTERN () else in_form t
           else
             Term.list_comb (Const c, map (in_term pat) ts)
       | (Free c, ts) => Term.list_comb (Free c, map (in_term pat) ts)
       | _ => t)
 
     and in_pat ((p as Const (\<^const_name>\<open>pat\<close>, _)) $ t) =
           p $ in_term true t
       | in_pat ((p as Const (\<^const_name>\<open>nopat\<close>, _)) $ t) =
           p $ in_term true t
       | in_pat t = raise TERM ("bad pattern", [t])
 
     and in_pats ps =
       in_list \<^typ>\<open>pattern symb_list\<close> (SOME o in_list \<^typ>\<open>pattern\<close> (try in_pat)) ps
 
     and in_trigger ((c as \<^Const_>\<open>trigger\<close>) $ p $ t) = c $ in_pats p $ in_form t
       | in_trigger t = in_form t
 
     and in_form t =
       (case Term.strip_comb t of
         (q as Const (qn, _), [Abs (n, T, u)]) =>
           if is_quant qn then q $ Abs (n, T, in_trigger u)
           else in_term false t
       | (Const c, ts) =>
           (case SMT_Builtin.dest_builtin_conn ctxt c ts of
             SOME (_, _, us, mk) => mk (map in_form us)
           | NONE =>
               (case SMT_Builtin.dest_builtin_pred ctxt c ts of
                 SOME (_, _, us, mk) => mk (map (in_term false) us)
               | NONE => in_term false t))
       | _ => in_term false t)
   in
     map (apsnd in_form) #>
     pair (fol_rules, I)
   end
 
 end
 
 
 (* translation into intermediate format *)
 
 (** utility functions **)
 
 val quantifier = (fn
     \<^const_name>\<open>All\<close> => SOME SForall
   | \<^const_name>\<open>Ex\<close> => SOME SExists
   | _ => NONE)
 
 fun group_quant qname Ts (t as Const (q, _) $ Abs (_, T, u)) =
       if q = qname then group_quant qname (T :: Ts) u else (Ts, t)
   | group_quant _ Ts t = (Ts, t)
 
 fun dest_pat (Const (\<^const_name>\<open>pat\<close>, _) $ t) = (t, true)
   | dest_pat (Const (\<^const_name>\<open>nopat\<close>, _) $ t) = (t, false)
   | dest_pat t = raise TERM ("bad pattern", [t])
 
 fun dest_pats [] = I
   | dest_pats ts =
       (case map dest_pat ts |> split_list ||> distinct (op =) of
         (ps, [true]) => cons (SPat ps)
       | (ps, [false]) => cons (SNoPat ps)
       | _ => raise TERM ("bad multi-pattern", ts))
 
 fun dest_trigger \<^Const_>\<open>trigger for tl t\<close> =
       (rev (fold (dest_pats o SMT_Util.dest_symb_list) (SMT_Util.dest_symb_list tl) []), t)
   | dest_trigger t = ([], t)
 
 fun dest_quant qn T t = quantifier qn |> Option.map (fn q =>
   let
     val (Ts, u) = group_quant qn [T] t
     val (ps, p) = dest_trigger u
   in (q, rev Ts, ps, p) end)
 
 fun fold_map_pat f (SPat ts) = fold_map f ts #>> SPat
   | fold_map_pat f (SNoPat ts) = fold_map f ts #>> SNoPat
 
 
 (** translation from Isabelle terms into SMT intermediate terms **)
 
 fun intermediate logic dtyps builtin ctxt ts trx =
   let
     fun transT (T as TFree _) = add_typ T true
       | transT (T as TVar _) = (fn _ => raise TYPE ("bad SMT type", [T], []))
       | transT (T as Type _) =
           (case SMT_Builtin.dest_builtin_typ ctxt T of
             SOME (n, []) => pair n
           | SOME (n, Ts) =>
             fold_map transT Ts
             #>> (fn ns => enclose "(" ")" (space_implode " " (n :: ns)))
           | NONE => add_typ T true)
 
     fun trans t =
       (case Term.strip_comb t of
         (Const (qn, _), [Abs (_, T, t1)]) =>
           (case dest_quant qn T t1 of
             SOME (q, Ts, ps, b) =>
               fold_map transT Ts ##>> fold_map (fold_map_pat trans) ps ##>>
               trans b #>> (fn ((Ts', ps'), b') => SQua (q, Ts', ps', b'))
           | NONE => raise TERM ("unsupported quantifier", [t]))
       | (u as Const (c as (_, T)), ts) =>
           (case builtin ctxt c ts of
             SOME (n, _, us, _) => fold_map trans us #>> curry SConst n
           | NONE => trans_applied_fun u T ts)
       | (u as Free (_, T), ts) => trans_applied_fun u T ts
       | (Bound i, ts) => pair i ##>> fold_map trans ts #>> SVar
       | _ => raise TERM ("bad SMT term", [t]))
 
     and trans_applied_fun t T ts =
       let val (Us, U) = SMT_Util.dest_funT (length ts) T
       in
         fold_map transT Us ##>> transT U #-> (fn Up =>
           add_fun t (SOME Up) ##>> fold_map trans ts #>> SConst)
       end
 
     val (us, trx') = fold_map (fn (role, t) => apfst (pair role) o trans t) ts trx
   in ((sign_of (logic ts) dtyps trx', us), trx') end
 
 
 (* translation *)
 
 structure Configs = Generic_Data
 (
   type T = (Proof.context -> config) SMT_Util.dict
   val empty = []
   fun merge data = SMT_Util.dict_merge fst data
 )
 
 fun add_config (cs, cfg) = Configs.map (SMT_Util.dict_update (cs, cfg))
 
 fun get_config ctxt =
   let val cs = SMT_Config.solver_class_of ctxt
   in
     (case SMT_Util.dict_get (Configs.get (Context.Proof ctxt)) cs of
       SOME cfg => cfg ctxt
     | NONE => error ("SMT: no translation configuration found " ^
         "for solver class " ^ quote (SMT_Util.string_of_class cs)))
   end
 
 fun translate ctxt prover smt_options comments (ithms : ((int * SMT_Util.role) * thm) list) =
   let
     val {order, logic, fp_kinds, serialize} = get_config ctxt
 
     fun no_dtyps (tr_context, ctxt) ts =
       ((Termtab.empty, [], tr_context, ctxt), ts)
 
     val ts1 = map (SMT_Util.map_prod snd (Envir.beta_eta_contract o SMT_Util.prop_of)) ithms
 
     val ((funcs, dtyps, tr_context, ctxt1), ts2) =
       ((empty_tr_context, ctxt), ts1)
       |-> (if null fp_kinds then no_dtyps else collect_co_datatypes fp_kinds)
 
     fun is_binder (Const (\<^const_name>\<open>Let\<close>, _) $ _) = true
       | is_binder t = Lambda_Lifting.is_quantifier t
 
     fun mk_trigger ((q as Const (\<^const_name>\<open>All\<close>, _)) $ Abs (n, T, t)) =
           q $ Abs (n, T, mk_trigger t)
       | mk_trigger (eq as (Const (\<^const_name>\<open>HOL.eq\<close>, T) $ lhs $ _)) =
           Term.domain_type T --> \<^typ>\<open>pattern\<close>
           |> (fn T => Const (\<^const_name>\<open>pat\<close>, T) $ lhs)
           |> SMT_Util.mk_symb_list \<^typ>\<open>pattern\<close> o single
           |> SMT_Util.mk_symb_list \<^typ>\<open>pattern symb_list\<close> o single
           |> (fn t => \<^Const>\<open>trigger for t eq\<close>)
       | mk_trigger t = t
 
     val (ctxt2, (ts3, ll_defs)) =
       ts2
       |> eta_expand ctxt1 funcs
       |> rpair ctxt1
       |-> Lambda_Lifting.lift_lambdas' NONE is_binder
       |-> (fn (ts', ll_defs) => fn ctxt' =>
         let
           val ts'' = map (pair SMT_Util.Axiom o mk_trigger) ll_defs @ ts'
             |> order = SMT_Util.First_Order ? intro_explicit_application ctxt' funcs
         in
           (ctxt', (ts'', ll_defs))
         end)
     val ((rewrite_rules, builtin), ts4) = folify ctxt2 ts3
       |>> order = SMT_Util.First_Order ? apfst (cons fun_app_eq)
   in
     (ts4, tr_context)
     |-> intermediate (logic prover o map snd) dtyps (builtin SMT_Builtin.dest_builtin) ctxt2
     |>> uncurry (serialize smt_options comments)
     ||> replay_data_of ctxt2 ll_defs rewrite_rules ithms
   end
 
 end;