diff -r f4815812665b -r e61b058d58d2 src/HOL/Subst/Subst.ML --- a/src/HOL/Subst/Subst.ML Thu Mar 23 15:39:13 1995 +0100 +++ b/src/HOL/Subst/Subst.ML Fri Mar 24 12:30:35 1995 +0100 @@ -19,9 +19,9 @@ ["Const(c) <| al = Const(c)", "Comb t u <| al = Comb (t <| al) (u <| al)", "[] <> bl = bl", - "(#al) <> bl = # (al <> bl)", + "((a,b)#al) <> bl = (a,b <| bl) # (al <> bl)", "sdom([]) = {}", - "sdom(#al) = (if Var(a)=b then (sdom al) Int Compl({a}) \ + "sdom((a,b)#al) = (if Var(a)=b then (sdom al) Int Compl({a}) \ \ else (sdom al) Un {a})" ]; (* This rewrite isn't always desired *) @@ -42,10 +42,10 @@ by (ALLGOALS (asm_simp_tac subst_ss)); val subst_mono = store_thm("subst_mono", result() RS mp); -goal Subst.thy "~ (Var(v) <: t) --> t <| #s = t <| s"; +goal Subst.thy "~ (Var(v) <: t) --> t <| (v,t <| s)#s = t <| s"; by (imp_excluded_middle_tac "t = Var(v)" 1); by (res_inst_tac [("P", - "%x.~x=Var(v) --> ~(Var(v) <: x) --> x <| #s=x<|s")] + "%x.~x=Var(v) --> ~(Var(v) <: x) --> x <| (v,t<|s)#s=x<|s")] uterm_induct 2); by (ALLGOALS (simp_tac (subst_ss addsimps [Var_subst]))); by (fast_tac HOL_cs 1); @@ -59,13 +59,13 @@ by (ALLGOALS (fast_tac HOL_cs)); qed "agreement"; -goal Subst.thy "~ v: vars_of(t) --> t <| #s = t <| s"; +goal Subst.thy "~ v: vars_of(t) --> t <| (v,u)#s = t <| s"; by(simp_tac(subst_ss addsimps [agreement,Var_subst] setloop (split_tac [expand_if])) 1); val repl_invariance = store_thm("repl_invariance", result() RS mp); val asms = goal Subst.thy - "v : vars_of(t) --> w : vars_of(t <| #s)"; + "v : vars_of(t) --> w : vars_of(t <| (v,Var(w))#s)"; by (uterm_ind_tac "t" 1); by (ALLGOALS (asm_simp_tac (subst_ss addsimps [Var_subst]))); val Var_in_subst = store_thm("Var_in_subst", result() RS mp); @@ -113,7 +113,7 @@ by (simp_tac (subst_ss addsimps [subst_eq_iff,subst_comp]) 1); qed "comp_assoc"; -goal Subst.thy "#s =s= s"; +goal Subst.thy "(w,Var(w) <| s)#s =s= s"; by (rtac (allI RS (subst_eq_iff RS iffD2)) 1); by (uterm_ind_tac "t" 1); by (REPEAT (etac rev_mp 3));