--- a/src/ZF/simpdata.ML Fri Jun 06 10:47:16 1997 +0200
+++ b/src/ZF/simpdata.ML Fri Jun 06 12:48:21 1997 +0200
@@ -8,45 +8,60 @@
(** Rewriting **)
-(*For proving rewrite rules*)
-fun prove_fun s =
- (writeln s; prove_goal ZF.thy s
- (fn prems => [ (cut_facts_tac prems 1), (Fast_tac 1) ]));
+local
+ (*For proving rewrite rules*)
+ fun prover s = (prove_goal ZF.thy s (fn _ => [Blast_tac 1]));
+
+in
-(*Are all these really suitable?*)
-val ball_simps = map prove_fun
- ["(ALL x:0.P(x)) <-> True",
+val ball_simps = map prover
+ ["(ALL x:A. P(x) | Q) <-> ((ALL x:A. P(x)) | Q)",
+ "(ALL x:A. P | Q(x)) <-> (P | (ALL x:A. Q(x)))",
+ "(ALL x:A. P --> Q(x)) <-> (P --> (ALL x:A. Q(x)))",
+ "(ALL x:A. P(x) --> Q) <-> ((EX x:A. P(x)) --> Q)",
+ "(ALL x:0.P(x)) <-> True",
"(ALL x:succ(i).P(x)) <-> P(i) & (ALL x:i.P(x))",
"(ALL x:cons(a,B).P(x)) <-> P(a) & (ALL x:B.P(x))",
"(ALL x:RepFun(A,f). P(x)) <-> (ALL y:A. P(f(y)))",
"(ALL x:Union(A).P(x)) <-> (ALL y:A. ALL x:y. P(x))",
"(ALL x:Collect(A,Q).P(x)) <-> (ALL x:A. Q(x) --> P(x))"];
-val bex_simps = map prove_fun
- ["(EX x:0.P(x)) <-> False",
+val ball_conj_distrib =
+ prover "(ALL x:A. P(x) & Q(x)) <-> ((ALL x:A. P(x)) & (ALL x:A. Q(x)))";
+
+val bex_simps = map prover
+ ["(EX x:A. P(x) & Q) <-> ((EX x:A. P(x)) & Q)",
+ "(EX x:A. P & Q(x)) <-> (P & (EX x:A. Q(x)))",
+ "(EX x:0.P(x)) <-> False",
"(EX x:succ(i).P(x)) <-> P(i) | (EX x:i.P(x))",
"(EX x:cons(a,B).P(x)) <-> P(a) | (EX x:B.P(x))",
"(EX x:RepFun(A,f). P(x)) <-> (EX y:A. P(f(y)))",
"(EX x:Union(A).P(x)) <-> (EX y:A. EX x:y. P(x))",
"(EX x:Collect(A,Q).P(x)) <-> (EX x:A. Q(x) & P(x))"];
-Addsimps (ball_simps @ bex_simps);
+val bex_disj_distrib =
+ prover "(EX x:A. P(x) | Q(x)) <-> ((EX x:A. P(x)) | (EX x:A. Q(x)))";
+
+val Rep_simps = map prover
+ ["{x:0. P(x)} = 0",
+ "{x:A. False} = 0",
+ "{x:A. True} = A",
+ "RepFun(0,f) = 0",
+ "RepFun(succ(i),f) = cons(f(i), RepFun(i,f))",
+ "RepFun(cons(a,B),f) = cons(f(a), RepFun(B,f))"]
-Addsimps (map prove_fun
- ["{x:0. P(x)} = 0",
- "{x:A. False} = 0",
- "{x:A. True} = A",
- "RepFun(0,f) = 0",
- "RepFun(succ(i),f) = cons(f(i), RepFun(i,f))",
- "RepFun(cons(a,B),f) = cons(f(a), RepFun(B,f))"]);
+val misc_simps = map prover
+ ["0 Un A = A", "A Un 0 = A",
+ "0 Int A = 0", "A Int 0 = 0",
+ "0-A = 0", "A-0 = A",
+ "Union(0) = 0",
+ "Union(cons(b,A)) = b Un Union(A)",
+ "Inter({b}) = b"]
-Addsimps (map prove_fun
- ["0 Un A = A", "A Un 0 = A",
- "0 Int A = 0", "A Int 0 = 0",
- "0-A = 0", "A-0 = A",
- "Union(0) = 0",
- "Union(cons(b,A)) = b Un Union(A)",
- "Inter({b}) = b"]);
+end;
+
+Addsimps (ball_simps @ bex_simps @ Rep_simps @ misc_simps);
+
(** New version of mk_rew_rules **)