src/HOLCF/Discrete1.ML

Simplified proofs by omitting PA = {|XA, ...|} from RA2

(*  Title:      HOLCF/Discrete1.ML
    ID:         $Id$
    Author:     Tobias Nipkow
    Copyright   1997 TUM

Proves that 'a discr is a cpo
*)

goalw thy [less_discr_def] "((x::('a::term)discr) << y) = (x=y)";
by (rtac refl 1);
qed "discr_less_eq";
AddIffs [discr_less_eq];

goalw thy [is_chain]
 "!!S::nat=>('a::term)discr. is_chain S ==> S i = S 0";
by (nat_ind_tac "i" 1);
by (rtac refl 1);
by (etac subst 1);
by (rtac sym 1);
by (Fast_tac 1);
qed "discr_chain0";

goal thy
 "!!S::nat=>('a::term)discr. is_chain(S) ==> range(S) = {S 0}";
by (fast_tac (claset() addEs [discr_chain0]) 1);
qed "discr_chain_range0";
Addsimps [discr_chain_range0];

goalw thy [is_lub,is_ub]
 "!!S. is_chain S ==> ? x::('a::term)discr. range(S) <<| x";
by (Asm_simp_tac 1);
qed "discr_cpo";