(* Title: HOLCF/ex/Fix2.thy
ID: $Id: Fix2.thy,v 1.7 2005/09/06 17:28:58 wenzelm Exp $
Author: Franz Regensburger
Show that fix is the unique least fixed-point operator.
From axioms gix1_def,gix2_def it follows that fix = gix
*)
theory Fix2
imports HOLCF
begin
consts
gix :: "('a->'a)->'a"
axioms
gix1_def: "F$(gix$F) = gix$F"
gix2_def: "F$y=y ==> gix$F << y"
ML {* use_legacy_bindings (the_context ()) *}
end
theorem lemma1:
fix = gix
theorem lemma2:
gix·F = (LUB i. iterate i F UU)