--- a/src/CCL/Gfp.ML Fri Oct 10 16:29:41 1997 +0200
+++ b/src/CCL/Gfp.ML Fri Oct 10 17:10:12 1997 +0200
@@ -71,13 +71,13 @@
- instead of the condition A <= f(A)
consider A <= (f(A) Un f(f(A)) ...) Un gfp(A) ***)
-val [prem] = goal Gfp.thy "mono(f) ==> mono(%x.f(x) Un A Un B)";
+val [prem] = goal Gfp.thy "mono(f) ==> mono(%x. f(x) Un A Un B)";
by (REPEAT (ares_tac [subset_refl, monoI, Un_mono, prem RS monoD] 1));
qed "coinduct3_mono_lemma";
val [prem,mono] = goal Gfp.thy
- "[| A <= f(lfp(%x.f(x) Un A Un gfp(f))); mono(f) |] ==> \
-\ lfp(%x.f(x) Un A Un gfp(f)) <= f(lfp(%x.f(x) Un A Un gfp(f)))";
+ "[| A <= f(lfp(%x. f(x) Un A Un gfp(f))); mono(f) |] ==> \
+\ lfp(%x. f(x) Un A Un gfp(f)) <= f(lfp(%x. f(x) Un A Un gfp(f)))";
by (rtac subset_trans 1);
by (rtac (mono RS coinduct3_mono_lemma RS lfp_lemma3) 1);
by (rtac (Un_least RS Un_least) 1);
@@ -90,7 +90,7 @@
qed "coinduct3_lemma";
val ainA::prems = goal Gfp.thy
- "[| a:A; A <= f(lfp(%x.f(x) Un A Un gfp(f))); mono(f) |] ==> a : gfp(f)";
+ "[| a:A; A <= f(lfp(%x. f(x) Un A Un gfp(f))); mono(f) |] ==> a : gfp(f)";
by (rtac coinduct 1);
by (rtac (prems MRS coinduct3_lemma) 2);
by (resolve_tac (prems RL [coinduct3_mono_lemma RS lfp_Tarski RS ssubst]) 1);
@@ -118,7 +118,7 @@
qed "def_coinduct2";
val rew::prems = goal Gfp.thy
- "[| h==gfp(f); a:A; A <= f(lfp(%x.f(x) Un A Un h)); mono(f) |] ==> a: h";
+ "[| h==gfp(f); a:A; A <= f(lfp(%x. f(x) Un A Un h)); mono(f) |] ==> a: h";
by (rewtac rew);
by (REPEAT (ares_tac (map (rewrite_rule [rew]) prems @ [coinduct3]) 1));
qed "def_coinduct3";