src/HOL/Subst/UTLemmas.ML
author nipkow
Mon Oct 21 09:50:50 1996 +0200 (1996-10-21)
changeset 2115 9709f9188549
parent 1465 5d7a7e439cec
permissions -rw-r--r--
Added trans_tac (see Provers/nat_transitive.ML)
     1 (*  Title:      HOL/Subst/UTLemmas.ML
     2     ID:         $Id$
     3     Author:     Martin Coen, Cambridge University Computer Laboratory
     4     Copyright   1993  University of Cambridge
     5 
     6 For UTLemmas.thy.  
     7 *)
     8 
     9 open UTLemmas;
    10 
    11 (***********)
    12 
    13 val utlemmas_defs = [vars_of_def, occs_def];
    14 
    15 local fun mk_thm s = prove_goalw UTLemmas.thy utlemmas_defs s 
    16                                  (fn _ => [Simp_tac 1])
    17 in val utlemmas_rews = map mk_thm 
    18       ["vars_of(Const(c)) = {}",
    19        "vars_of(Var(x)) = {x}",
    20        "vars_of(Comb t u) = vars_of(t) Un vars_of(u)",
    21        "t <: Const(c) = False",
    22        "t <: Var(x) = False",
    23        "t <: Comb u v = (t=u | t=v | t <: u | t <: v)"];
    24 end;
    25 
    26 Addsimps (setplus_rews @ uterm_rews @ utlemmas_rews);
    27 
    28 (****  occs irrefl ****)
    29 
    30 goal UTLemmas.thy  "t <: u & u <: v --> t <: v";
    31 by (uterm_ind_tac "v" 1);
    32 by (ALLGOALS Simp_tac);
    33 by (fast_tac HOL_cs 1);
    34 val occs_trans  = store_thm("occs_trans", conjI RS (result() RS mp));
    35 
    36 goal UTLemmas.thy   "~ t <: v --> ~ t <: u | ~ u <: v";
    37 by (fast_tac (HOL_cs addIs [occs_trans]) 1);
    38 val contr_occs_trans  = store_thm("contr_occs_trans", result() RS mp);
    39 
    40 goal UTLemmas.thy   "t <: Comb t u";
    41 by (Simp_tac 1);
    42 qed "occs_Comb1";
    43 
    44 goal UTLemmas.thy  "u <: Comb t u";
    45 by (Simp_tac 1);
    46 qed "occs_Comb2";
    47 
    48 goal HOL.thy  "(~(P|Q)) = (~P & ~Q)";
    49 by (fast_tac HOL_cs 1);
    50 qed "demorgan_disj";
    51 
    52 goal UTLemmas.thy  "~ t <: t";
    53 by (uterm_ind_tac "t" 1);
    54 by (ALLGOALS (simp_tac (!simpset addsimps [demorgan_disj])));
    55 by (REPEAT (resolve_tac [impI,conjI] 1 ORELSE
    56             (etac contrapos 1 THEN etac subst 1 THEN 
    57              resolve_tac [occs_Comb1,occs_Comb2] 1) ORELSE
    58             (etac (contr_occs_trans RS disjE) 1 THEN assume_tac 2) ORELSE
    59             eresolve_tac ([occs_Comb1,occs_Comb2] RLN(2,[notE])) 1));
    60 qed "occs_irrefl";
    61 
    62 goal UTLemmas.thy  "t <: u --> ~t=u";
    63 by (fast_tac (HOL_cs addEs [occs_irrefl RS notE]) 1);
    64 val occs_irrefl2  = store_thm("occs_irrefl2", result() RS mp);
    65 
    66 
    67 (**** vars_of lemmas  ****)
    68 
    69 goal UTLemmas.thy "(v : vars_of(Var(w))) = (w=v)";
    70 by (Simp_tac 1);
    71 by (fast_tac HOL_cs 1);
    72 qed "vars_var_iff";
    73 
    74 goal UTLemmas.thy  "(x : vars_of(t)) = (Var(x) <: t | Var(x) = t)";
    75 by (uterm_ind_tac "t" 1);
    76 by (ALLGOALS Simp_tac);
    77 by (fast_tac HOL_cs 1);
    78 qed "vars_iff_occseq";