src/HOLCF/Discrete1.ML

-(*  Title:      HOLCF/Discrete1.ML
-    ID:         $Id$
-    Author:     Tobias Nipkow
-
-Proves that 'a discr is a cpo
-*)
-
-Goalw [less_discr_def] "((x::('a::type)discr) << y) = (x=y)";
-by (rtac refl 1);
-qed "discr_less_eq";
-AddIffs [discr_less_eq];
-
-Goalw [chain_def]
- "!!S::nat=>('a::type)discr. chain S ==> S i = S 0";
-by (induct_tac "i" 1);
-by (rtac refl 1);
-by (etac subst 1);
-by (rtac sym 1);
-by (Fast_tac 1);
-qed "discr_chain0";
-
-Goal
- "!!S::nat=>('a::type)discr. chain(S) ==> range(S) = {S 0}";
-by (fast_tac (claset() addEs [discr_chain0]) 1);
-qed "discr_chain_range0";
-Addsimps [discr_chain_range0];
-
-Goalw [is_lub_def,is_ub_def]
- "!!S. chain S ==> ? x::('a::type)discr. range(S) <<| x";
-by (Asm_simp_tac 1);
-qed "discr_cpo";