src/HOL/HOLCF/ex/Fix2.thy
changeset 40774 0437dbc127b3
parent 40431 682d6c455670
child 42151 4da4fc77664b
     1.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
     1.2 +++ b/src/HOL/HOLCF/ex/Fix2.thy	Sat Nov 27 16:08:10 2010 -0800
     1.3 @@ -0,0 +1,32 @@
     1.4 +(*  Title:      HOLCF/ex/Fix2.thy
     1.5 +    Author:     Franz Regensburger
     1.6 +
     1.7 +Show that fix is the unique least fixed-point operator.
     1.8 +From axioms gix1_def,gix2_def it follows that fix = gix
     1.9 +*)
    1.10 +
    1.11 +theory Fix2
    1.12 +imports HOLCF
    1.13 +begin
    1.14 +
    1.15 +axiomatization
    1.16 +  gix :: "('a->'a)->'a" where
    1.17 +  gix1_def: "F$(gix$F) = gix$F" and
    1.18 +  gix2_def: "F$y=y ==> gix$F << y"
    1.19 +
    1.20 +
    1.21 +lemma lemma1: "fix = gix"
    1.22 +apply (rule cfun_eqI)
    1.23 +apply (rule below_antisym)
    1.24 +apply (rule fix_least)
    1.25 +apply (rule gix1_def)
    1.26 +apply (rule gix2_def)
    1.27 +apply (rule fix_eq [symmetric])
    1.28 +done
    1.29 +
    1.30 +lemma lemma2: "gix$F=lub(range(%i. iterate i$F$UU))"
    1.31 +apply (rule lemma1 [THEN subst])
    1.32 +apply (rule fix_def2)
    1.33 +done
    1.34 +
    1.35 +end