src/Provers/eqsubst.ML
author dixon
Wed May 18 23:04:13 2005 +0200 (2005-05-18)
changeset 16004 031f56012483
parent 15959 366d39e95d3c
child 16007 4dcccaa11a13
permissions -rw-r--r--
lucas - fixed subst in assumptions to count redexes from left to right.
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(* -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- *) 
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(*  Title:      Provers/eqsubst.ML
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    Author:     Lucas Dixon, University of Edinburgh
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                lucas.dixon@ed.ac.uk
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    Modified:   18 Feb 2005 - Lucas - 
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    Created:    29 Jan 2005
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*)
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(* -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- *) 
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(*  DESCRIPTION:
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    A Tactic to perform a substiution using an equation.
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*)
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(* -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- *)
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(* Logic specific data stub *)
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signature EQRULE_DATA =
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sig
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  (* to make a meta equality theorem in the current logic *)
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  val prep_meta_eq : thm -> thm list
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end;
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(* the signature of an instance of the SQSUBST tactic *)
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signature EQSUBST_TAC = 
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sig
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  exception eqsubst_occL_exp of 
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            string * (int list) * (Thm.thm list) * int * Thm.thm;
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  type match = 
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       ((Term.indexname * (Term.sort * Term.typ)) list (* type instantiations *)
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        * (Term.indexname * (Term.typ * Term.term)) list) (* term instantiations *)
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       * (string * Term.typ) list (* fake named type abs env *)
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       * (string * Term.typ) list (* type abs env *)
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       * Term.term (* outer term *)
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  type searchinfo = 
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       Sign.sg (* sign for matching *)
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       * int (* maxidx *)
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       * BasicIsaFTerm.FcTerm (* focusterm to search under *)
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  val prep_subst_in_asm :
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         int (* subgoal to subst in *)
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      -> Thm.thm (* target theorem with subgoals *)
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      -> int (* premise to subst in *)
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      -> (Thm.cterm list (* certified free var placeholders for vars *) 
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          * int (* premice no. to subst *)
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          * int (* number of assumptions of premice *)
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          * Thm.thm) (* premice as a new theorem for forward reasoning *)
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         * searchinfo (* search info: prem id etc *)
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  val prep_subst_in_asms :
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         int (* subgoal to subst in *)
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      -> Thm.thm (* target theorem with subgoals *)
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      -> ((Thm.cterm list (* certified free var placeholders for vars *) 
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          * int (* premice no. to subst *)
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          * int (* number of assumptions of premice *)
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          * Thm.thm) (* premice as a new theorem for forward reasoning *)
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         * searchinfo) list
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  val apply_subst_in_asm :
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      int (* subgoal *)
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      -> Thm.thm (* overall theorem *)
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      -> Thm.thm (* rule *)
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      -> (Thm.cterm list (* certified free var placeholders for vars *) 
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          * int (* assump no being subst *)
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          * int (* num of premises of asm *) 
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          * Thm.thm) (* premthm *)
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      * match
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      -> Thm.thm Seq.seq
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  val prep_concl_subst :
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         int (* subgoal *)
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      -> Thm.thm (* overall goal theorem *)
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      -> (Thm.cterm list * Thm.thm) * searchinfo (* (cvfs, conclthm), matchf *)
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  val apply_subst_in_concl :
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        int (* subgoal *)
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        -> Thm.thm (* thm with all goals *)
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        -> Thm.cterm list (* certified free var placeholders for vars *)
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           * Thm.thm  (* trivial thm of goal concl *)
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            (* possible matches/unifiers *)
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        -> Thm.thm (* rule *)
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        -> match
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        -> Thm.thm Seq.seq (* substituted goal *)
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  (* basic notion of search *)
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  val searchf_tlr_unify_all : 
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      (searchinfo 
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       -> Term.term (* lhs *)
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       -> match Seq.seq Seq.seq)
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  val searchf_tlr_unify_valid : 
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      (searchinfo 
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       -> Term.term (* lhs *)
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       -> match Seq.seq Seq.seq)
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  (* specialise search constructor for conclusion skipping occurnaces. *)
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     val skip_first_occs_search :
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        int -> ('a -> 'b -> 'c Seq.seq Seq.seq) -> 'a -> 'b -> 'c Seq.seq
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  (* specialised search constructor for assumptions using skips *)
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     val skip_first_asm_occs_search :
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        ('a -> 'b -> 'c Seq.seq Seq.seq) ->
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        'a -> int -> 'b -> 'c IsaPLib.skipseqT
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  (* tactics and methods *)
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  val eqsubst_asm_meth : int list -> Thm.thm list -> Proof.method
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  val eqsubst_asm_tac : 
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      int list -> Thm.thm list -> int -> Thm.thm -> Thm.thm Seq.seq
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  val eqsubst_asm_tac' : 
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      (* search function with skips *)
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      (searchinfo -> int -> Term.term -> match IsaPLib.skipseqT) 
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      -> int (* skip to *)
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      -> Thm.thm (* rule *)
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      -> int (* subgoal number *)
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      -> Thm.thm (* tgt theorem with subgoals *)
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      -> Thm.thm Seq.seq (* new theorems *)
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  val eqsubst_meth : int list -> Thm.thm list -> Proof.method
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  val eqsubst_tac : 
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      int list -> Thm.thm list -> int -> Thm.thm -> Thm.thm Seq.seq
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  val eqsubst_tac' : 
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      (searchinfo -> Term.term -> match Seq.seq) 
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      -> Thm.thm -> int -> Thm.thm -> Thm.thm Seq.seq
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  val meth : (bool * int list) * Thm.thm list -> Proof.context -> Proof.method
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  val setup : (Theory.theory -> Theory.theory) list
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end;
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functor EQSubstTacFUN (structure EqRuleData : EQRULE_DATA) 
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  : EQSUBST_TAC
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= struct
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  (* a type abriviation for match information *)
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  type match = 
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       ((Term.indexname * (Term.sort * Term.typ)) list (* type instantiations *)
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        * (Term.indexname * (Term.typ * Term.term)) list) (* term instantiations *)
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       * (string * Term.typ) list (* fake named type abs env *)
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       * (string * Term.typ) list (* type abs env *)
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       * Term.term (* outer term *)
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  type searchinfo = 
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       Sign.sg (* sign for matching *)
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       * int (* maxidx *)
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       * BasicIsaFTerm.FcTerm (* focusterm to search under *)
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(* FOR DEBUGGING...
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type trace_subst_errT = int (* subgoal *)
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        * Thm.thm (* thm with all goals *)
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        * (Thm.cterm list (* certified free var placeholders for vars *)
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           * Thm.thm)  (* trivial thm of goal concl *)
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            (* possible matches/unifiers *)
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        * Thm.thm (* rule *)
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        * (((Term.indexname * Term.typ) list (* type instantiations *)
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              * (Term.indexname * Term.term) list ) (* term instantiations *)
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             * (string * Term.typ) list (* Type abs env *)
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             * Term.term) (* outer term *);
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val trace_subst_err = (ref NONE : trace_subst_errT option ref);
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val trace_subst_search = ref false;
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exception trace_subst_exp of trace_subst_errT;
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 *)
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(* also defined in /HOL/Tools/inductive_codegen.ML, 
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   maybe move this to seq.ML ? *)
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infix 5 :->;
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fun s :-> f = Seq.flat (Seq.map f s);
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(* search from top, left to right, then down *)
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fun search_tlr_all_f f ft = 
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    let
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      fun maux ft = 
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          let val t' = (IsaFTerm.focus_of_fcterm ft) 
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            (* val _ = 
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                if !trace_subst_search then 
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                  (writeln ("Examining: " ^ (TermLib.string_of_term t'));
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                   TermLib.writeterm t'; ())
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                else (); *)
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          in 
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          (case t' of 
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            (_ $ _) => Seq.append(maux (IsaFTerm.focus_left ft), 
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                       Seq.cons(f ft, 
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                                  maux (IsaFTerm.focus_right ft)))
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          | (Abs _) => Seq.cons(f ft, maux (IsaFTerm.focus_abs ft))
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          | leaf => Seq.single (f ft)) end
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    in maux ft end;
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(* search from top, left to right, then down *)
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fun search_tlr_valid_f f ft = 
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    let
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      fun maux ft = 
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          let 
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            val hereseq = if IsaFTerm.valid_match_start ft then f ft else Seq.empty
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          in 
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          (case (IsaFTerm.focus_of_fcterm ft) of 
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            (_ $ _) => Seq.append(maux (IsaFTerm.focus_left ft), 
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                       Seq.cons(hereseq, 
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                                  maux (IsaFTerm.focus_right ft)))
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          | (Abs _) => Seq.cons(hereseq, maux (IsaFTerm.focus_abs ft))
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          | leaf => Seq.single (hereseq))
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          end
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    in maux ft end;
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(* search all unifications *)
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fun searchf_tlr_unify_all (sgn, maxidx, ft) lhs = 
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    IsaFTerm.find_fcterm_matches 
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      search_tlr_all_f 
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      (IsaFTerm.clean_unify_ft sgn maxidx lhs)
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      ft;
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(* search only for 'valid' unifiers (non abs subterms and non vars) *)
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fun searchf_tlr_unify_valid (sgn, maxidx, ft) lhs  = 
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    IsaFTerm.find_fcterm_matches 
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      search_tlr_valid_f 
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      (IsaFTerm.clean_unify_ft sgn maxidx lhs)
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      ft;
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(* apply a substitution in the conclusion of the theorem th *)
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(* cfvs are certified free var placeholders for goal params *)
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(* conclthm is a theorem of for just the conclusion *)
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(* m is instantiation/match information *)
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(* rule is the equation for substitution *)
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fun apply_subst_in_concl i th (cfvs, conclthm) rule m = 
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    (RWInst.rw m rule conclthm)
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      |> IsaND.unfix_frees cfvs
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      |> RWInst.beta_eta_contract
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      |> (fn r => Tactic.rtac r i th);
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(*
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 |> (fn r => Thm.bicompose false (false, r, Thm.nprems_of r) i th)
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*)
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(* substitute within the conclusion of goal i of gth, using a meta
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equation rule. Note that we assume rule has var indicies zero'd *)
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fun prep_concl_subst i gth = 
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    let 
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      val th = Thm.incr_indexes 1 gth;
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      val tgt_term = Thm.prop_of th;
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      val sgn = Thm.sign_of_thm th;
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      val ctermify = Thm.cterm_of sgn;
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      val trivify = Thm.trivial o ctermify;
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      val (fixedbody, fvs) = IsaND.fix_alls_term i tgt_term;
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      val cfvs = rev (map ctermify fvs);
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      val conclterm = Logic.strip_imp_concl fixedbody;
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      val conclthm = trivify conclterm;
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      val maxidx = Term.maxidx_of_term conclterm;
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      val ft = ((IsaFTerm.focus_right  
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                 o IsaFTerm.focus_left
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                 o IsaFTerm.fcterm_of_term 
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                 o Thm.prop_of) conclthm)
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    in
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      ((cfvs, conclthm), (sgn, maxidx, ft))
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    end;
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(* substitute using an object or meta level equality *)
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fun eqsubst_tac' searchf instepthm i th = 
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    let 
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      val (cvfsconclthm, searchinfo) = prep_concl_subst i th;
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      val stepthms = 
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          Seq.map Drule.zero_var_indexes 
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                  (Seq.of_list (EqRuleData.prep_meta_eq instepthm));
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      fun rewrite_with_thm r =
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          let val (lhs,_) = Logic.dest_equals (Thm.concl_of r);
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          in (searchf searchinfo lhs)
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             :-> (apply_subst_in_concl i th cvfsconclthm r) end;
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    in stepthms :-> rewrite_with_thm end;
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(* Tactic.distinct_subgoals_tac -- fails to free type variables *)
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(* custom version of distinct subgoals that works with term and 
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   type variables. Asssumes th is in beta-eta normal form. 
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   Also, does nothing if flexflex contraints are present. *)
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fun distinct_subgoals th =
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    if List.null (Thm.tpairs_of th) then
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      let val (fixes,fixedthm) = IsaND.fix_vars_and_tvars th
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        val (fixedthconcl,cprems) = IsaND.hide_prems fixedthm
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      in
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        IsaND.unfix_frees_and_tfrees 
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          fixes
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          (Drule.implies_intr_list 
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             (Library.gen_distinct 
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                (fn (x, y) => Thm.term_of x = Thm.term_of y)
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                cprems) fixedthconcl)
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      end
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    else th;
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(* General substiuttion of multiple occurances using one of 
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   the given theorems*)
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exception eqsubst_occL_exp of 
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          string * (int list) * (Thm.thm list) * int * Thm.thm;
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fun skip_first_occs_search occ srchf sinfo lhs = 
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    case (IsaPLib.skipto_seqseq occ (srchf sinfo lhs)) of 
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      IsaPLib.skipmore _ => Seq.empty
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    | IsaPLib.skipseq ss => Seq.flat ss;
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fun eqsubst_tac occL thms i th = 
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    let val nprems = Thm.nprems_of th in
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      if nprems < i then Seq.empty else
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      let val thmseq = (Seq.of_list thms) 
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        fun apply_occ occ th = 
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            thmseq :-> 
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                    (fn r => eqsubst_tac' (skip_first_occs_search 
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                                    occ searchf_tlr_unify_valid) r
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                                 (i + ((Thm.nprems_of th) - nprems))
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                                 th);
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        val sortedoccL = 
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            Library.sort (Library.rev_order o Library.int_ord) occL;
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      in
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        Seq.map distinct_subgoals (Seq.EVERY (map apply_occ sortedoccL) th)
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      end
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    end
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    handle THM _ => raise eqsubst_occL_exp ("THM",occL,thms,i,th);
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(* inthms are the given arguments in Isar, and treated as eqstep with
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   the first one, then the second etc *)
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fun eqsubst_meth occL inthms =
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    Method.METHOD 
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      (fn facts =>
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          HEADGOAL ( Method.insert_tac facts THEN' eqsubst_tac occL inthms ));
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(* apply a substitution inside assumption j, keeps asm in the same place *)
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fun apply_subst_in_asm i th rule ((cfvs, j, nprems, pth),m) = 
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    let 
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      val th2 = Thm.rotate_rule (j - 1) i th; (* put premice first *)
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      val preelimrule = 
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          (RWInst.rw m rule pth)
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            |> (Seq.hd o Tactic.prune_params_tac)
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            |> Thm.permute_prems 0 ~1 (* put old asm first *)
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            |> IsaND.unfix_frees cfvs (* unfix any global params *)
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            |> RWInst.beta_eta_contract; (* normal form *)
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      val elimrule = 
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          preelimrule
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            |> Tactic.make_elim (* make into elim rule *)
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            |> Thm.lift_rule (th2, i); (* lift into context *)
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    in
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      (* ~j because new asm starts at back, thus we subtract 1 *)
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      Seq.map (Thm.rotate_rule (~j) (nprems + i))
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              (Thm.bicompose 
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                 false (* use unification *)
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                 (true, (* elim resolution *)
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                  elimrule, 2 + nprems) 
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                 i th2)
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    end;
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(* prepare to substitute within the j'th premise of subgoal i of gth,
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using a meta-level equation. Note that we assume rule has var indicies
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zero'd. Note that we also assume that premt is the j'th premice of
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subgoal i of gth. Note the repetition of work done for each
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assumption, i.e. this can be made more efficient for search over
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multiple assumptions.  *)
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fun prep_subst_in_asm i gth j = 
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    let 
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      val th = Thm.incr_indexes 1 gth;
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      val tgt_term = Thm.prop_of th;
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      val sgn = Thm.sign_of_thm th;
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      val ctermify = Thm.cterm_of sgn;
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      val trivify = Thm.trivial o ctermify;
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      val (fixedbody, fvs) = IsaND.fix_alls_term i tgt_term;
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      val cfvs = rev (map ctermify fvs);
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      val asmt = Library.nth_elem(j - 1,(Logic.strip_imp_prems fixedbody));
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      val asm_nprems = length (Logic.strip_imp_prems asmt);
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      val pth = trivify asmt;
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      val maxidx = Term.maxidx_of_term asmt;
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      val ft = ((IsaFTerm.focus_right 
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                 o IsaFTerm.fcterm_of_term 
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                 o Thm.prop_of) pth)
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    in ((cfvs, j, asm_nprems, pth), (sgn, maxidx, ft)) end;
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(* prepare subst in every possible assumption *)
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fun prep_subst_in_asms i gth = 
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    map (prep_subst_in_asm i gth)
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        ((rev o IsaPLib.mk_num_list o length) 
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           (Logic.prems_of_goal (Thm.prop_of gth) i));
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(* substitute in an assumption using an object or meta level equality *)
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fun eqsubst_asm_tac' searchf skipocc instepthm i th = 
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    let 
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      val asmpreps = prep_subst_in_asms i th;
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      val stepthms = 
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          Seq.map Drule.zero_var_indexes 
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              (Seq.of_list (EqRuleData.prep_meta_eq instepthm))
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      fun rewrite_with_thm r =
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          let val (lhs,_) = Logic.dest_equals (Thm.concl_of r)
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            fun occ_search occ [] = Seq.empty
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              | occ_search occ ((asminfo, searchinfo)::moreasms) =
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                (case searchf searchinfo occ lhs of 
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                   IsaPLib.skipmore i => occ_search i moreasms
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                 | IsaPLib.skipseq ss => 
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                   Seq.append (Seq.map (Library.pair asminfo)
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                                       (Seq.flat ss), 
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                               occ_search 1 moreasms))
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                              (* find later substs also *)
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          in 
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            (occ_search skipocc asmpreps) :-> (apply_subst_in_asm i th r)
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          end;
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    in stepthms :-> rewrite_with_thm end;
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fun skip_first_asm_occs_search searchf sinfo occ lhs = 
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    IsaPLib.skipto_seqseq occ (searchf sinfo lhs);
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fun eqsubst_asm_tac occL thms i th = 
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    let val nprems = Thm.nprems_of th 
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    in
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      if nprems < i then Seq.empty else
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      let val thmseq = (Seq.of_list thms) 
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        fun apply_occ occK th = 
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            thmseq :-> 
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                    (fn r => 
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                        eqsubst_asm_tac' (skip_first_asm_occs_search 
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                                            searchf_tlr_unify_valid) occK r
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                                         (i + ((Thm.nprems_of th) - nprems))
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                                         th);
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        val sortedoccs = 
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            Library.sort (Library.rev_order o Library.int_ord) occL
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      in
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        Seq.map distinct_subgoals
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                (Seq.EVERY (map apply_occ sortedoccs) th)
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      end
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    end
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    handle THM _ => raise eqsubst_occL_exp ("THM",occL,thms,i,th);
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(* inthms are the given arguments in Isar, and treated as eqstep with
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   the first one, then the second etc *)
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fun eqsubst_asm_meth occL inthms =
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    Method.METHOD 
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      (fn facts =>
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          HEADGOAL (Method.insert_tac facts THEN' eqsubst_asm_tac occL inthms ));
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(* combination method that takes a flag (true indicates that subst
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should be done to an assumption, false = apply to the conclusion of
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the goal) as well as the theorems to use *)
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fun meth ((asmflag, occL), inthms) ctxt = 
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    if asmflag then eqsubst_asm_meth occL inthms else eqsubst_meth occL inthms;
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(* syntax for options, given "(asm)" will give back true, without
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   gives back false *)
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val options_syntax =
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    (Args.parens (Args.$$$ "asm") >> (K true)) ||
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     (Scan.succeed false);
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val ith_syntax =
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    (Args.parens (Scan.repeat Args.nat))
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      || (Scan.succeed [0]);
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(* method syntax, first take options, then theorems *)
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fun meth_syntax meth src ctxt =
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    meth (snd (Method.syntax ((Scan.lift options_syntax) 
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                                -- (Scan.lift ith_syntax) 
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                                -- Attrib.local_thms) src ctxt)) 
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         ctxt;
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(* setup function for adding method to theory. *)
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val setup = 
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    [Method.add_method ("subst", meth_syntax meth, "Substiution with an equation. Use \"(asm)\" option to substitute in an assumption.")];
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   475
end;