Subst/utlemmas.ML

changed "." to "$" and Cons to infix "#" to eliminate ambiguity

(*  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();