# File Fix2.ML

    (*  Title:      HOLCF/ex/Fix2.ML
        ID:         $Id: Fix2.ML,v 1.7 2005/09/06 17:28:58 wenzelm Exp $
        Author:     Franz Regensburger
    *)

    Goal "fix = gix";
    by (rtac ext_cfun 1);
    by (rtac antisym_less 1);
    by (rtac fix_least 1);
    by (rtac gix1_def 1);
    by (rtac gix2_def 1);
    by (rtac (fix_eq RS sym) 1);
    qed "lemma1";

    Goal "gix$F=lub(range(%i. iterate i F UU))";
    by (rtac (lemma1 RS subst) 1);
    by (rtac fix_def2 1);
    qed "lemma2";