diff -r f04b33ce250f -r a4dc62a46ee4 Subst/UTLemmas.ML --- 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";