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));