--- a/Subst/UTLemmas.ML Tue Oct 24 14:59:17 1995 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,77 +0,0 @@
-(* Title: Substitutions/UTLemmas.ML
- Author: Martin Coen, Cambridge University Computer Laboratory
- Copyright 1993 University of Cambridge
-
-For UTLemmas.thy.
-*)
-
-open UTLemmas;
-
-(***********)
-
-val utlemmas_defs = [vars_of_def,occs_def];
-
-local fun mk_thm s = prove_goalw UTLemmas.thy utlemmas_defs s
- (fn _ => [simp_tac uterm_ss 1])
-in val utlemmas_rews = map mk_thm
- ["vars_of(Const(c)) = {}",
- "vars_of(Var(x)) = {x}",
- "vars_of(Comb(t,u)) = vars_of(t) Un vars_of(u)",
- "t <: Const(c) = False",
- "t <: Var(x) = False",
- "t <: Comb(u,v) = (t=u | t=v | t <: u | t <: v)"];
-end;
-
-val utlemmas_ss = prod_ss addsimps (setplus_rews @ uterm_rews @ utlemmas_rews);
-
-(**** occs irrefl ****)
-
-goal UTLemmas.thy "t <: u & u <: v --> t <: v";
-by (uterm_ind_tac "v" 1);
-by (ALLGOALS (simp_tac utlemmas_ss));
-by (fast_tac HOL_cs 1);
-val occs_trans = store_thm("occs_trans", conjI RS (result() RS mp));
-
-goal UTLemmas.thy "~ t <: v --> ~ t <: u | ~ u <: v";
-by (fast_tac (HOL_cs addIs [occs_trans]) 1);
-val contr_occs_trans = store_thm("contr_occs_trans", result() RS mp);
-
-goal UTLemmas.thy "t <: Comb(t,u)";
-by (simp_tac utlemmas_ss 1);
-qed "occs_Comb1";
-
-goal UTLemmas.thy "u <: Comb(t,u)";
-by (simp_tac utlemmas_ss 1);
-qed "occs_Comb2";
-
-goal HOL.thy "(~(P|Q)) = (~P & ~Q)";
-by (fast_tac HOL_cs 1);
-qed "demorgan_disj";
-
-goal UTLemmas.thy "~ t <: t";
-by (uterm_ind_tac "t" 1);
-by (ALLGOALS (simp_tac (utlemmas_ss addsimps [demorgan_disj])));
-by (REPEAT (resolve_tac [impI,conjI] 1 ORELSE
- (etac contrapos 1 THEN etac subst 1 THEN
- resolve_tac [occs_Comb1,occs_Comb2] 1) ORELSE
- (etac (contr_occs_trans RS disjE) 1 THEN assume_tac 2) ORELSE
- eresolve_tac ([occs_Comb1,occs_Comb2] RLN(2,[notE])) 1));
-qed "occs_irrefl";
-
-goal UTLemmas.thy "t <: u --> ~t=u";
-by (fast_tac (HOL_cs addEs [occs_irrefl RS notE]) 1);
-val occs_irrefl2 = store_thm("occs_irrefl2", result() RS mp);
-
-
-(**** vars_of lemmas ****)
-
-goal UTLemmas.thy "(v : vars_of(Var(w))) = (w=v)";
-by (simp_tac utlemmas_ss 1);
-by (fast_tac HOL_cs 1);
-qed "vars_var_iff";
-
-goal UTLemmas.thy "(x : vars_of(t)) = (Var(x) <: t | Var(x) = t)";
-by (uterm_ind_tac "t" 1);
-by (ALLGOALS (simp_tac utlemmas_ss));
-by (fast_tac HOL_cs 1);
-qed "vars_iff_occseq";