src/LCF/ex/Ex1.ML

+
+simpset_ref() := LCF_ss;
+
+Addsimps [P_strict,K];
+
+val H_unfold = prove_goal thy "H = K(H)"
+ (fn _ => [stac H 1, rtac (FIX_eq RS sym) 1]);
+
+bind_thm ("H_unfold", H_unfold);
+
+
+val H_strict = prove_goal thy "H(UU)=UU"
+ (fn _ => [stac H_unfold 1, Simp_tac 1]);
+
+bind_thm ("H_strict", H_strict);
+Addsimps [H_strict];
+
+goal thy "ALL x. H(FIX(K,x)) = FIX(K,x)";
+by (induct_tac "K" 1);
+by (Simp_tac 1);
+by (simp_tac (simpset() setloop (split_tac [COND_cases_iff])) 1);
+by (strip_tac 1);
+by (stac H_unfold 1);
+by (Asm_simp_tac 1);
+qed "H_idemp_lemma";
+
+val H_idemp = rewrite_rule [mk_meta_eq (H RS sym)] H_idemp_lemma;
+bind_thm ("H_idemp", H_idemp);