--- a/src/LCF/ex/Ex2.thy Mon Mar 19 21:25:15 2012 +0100
+++ b/src/LCF/ex/Ex2.thy Mon Mar 19 21:49:52 2012 +0100
@@ -4,16 +4,15 @@
imports LCF
begin
-consts
- P :: "'a => tr"
- F :: "'a => 'a"
- G :: "'a => 'a"
- H :: "'a => 'b => 'b"
+axiomatization
+ P :: "'a => tr" and
+ F :: "'b => 'b" and
+ G :: "'a => 'a" and
+ H :: "'a => 'b => 'b" and
K :: "('a => 'b => 'b) => ('a => 'b => 'b)"
-
-axioms
- F_strict: "F(UU) = UU"
- K: "K = (%h x y. P(x) => y | F(h(G(x),y)))"
+where
+ F_strict: "F(UU) = UU" and
+ K: "K = (%h x y. P(x) => y | F(h(G(x),y)))" and
H: "H = FIX(K)"
declare F_strict [simp] K [simp]
@@ -21,8 +20,8 @@
lemma example: "ALL x. F(H(x::'a,y::'b)) = H(x,F(y))"
apply (simplesubst H)
apply (tactic {* induct_tac @{context} "K:: ('a=>'b=>'b) => ('a=>'b=>'b)" 1 *})
- apply (simp (no_asm))
- apply (simp (no_asm_simp) split: COND_cases_iff)
+ apply simp
+ apply (simp split: COND_cases_iff)
done
end