Subst/utlemmas.ML

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Subst/utlemmas.ML	Thu Sep 16 12:21:07 1993 +0200
@@ -0,0 +1,77 @@
+(*  Title: 	Substitutions/utermlemmas.ML
+    Author: 	Martin Coen, Cambridge University Computer Laboratory
+    Copyright   1993  University of Cambridge
+
+For utermlemmas.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 = pair_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 = 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 = result() RS mp;
+
+goal UTLemmas.thy   "t <: Comb(t,u)";
+by (simp_tac utlemmas_ss 1);
+val occs_Comb1 = result();
+
+goal UTLemmas.thy  "u <: Comb(t,u)";
+by (simp_tac utlemmas_ss 1);
+val occs_Comb2 = result();
+
+goal HOL.thy  "(~(P|Q)) = (~P & ~Q)";
+by (fast_tac HOL_cs 1);
+val demorgan_disj = result();
+
+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));
+val occs_irrefl = result();
+
+goal UTLemmas.thy  "t <: u --> ~t=u";
+by (fast_tac (HOL_cs addEs [occs_irrefl RS notE]) 1);
+val 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);
+val vars_var_iff = result();
+
+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);
+val vars_iff_occseq = result();