isabelle: src/HOLCF/ex/Fix2.thy@ec2a8efd8990 (annotated)

1479 21eb5e156d91 expanded tabs clasohm parents: 1274 diff changeset	1	(* Title: HOLCF/ex/Fix2.thy
21eb5e156d91 expanded tabs clasohm parents: 1274 diff changeset	2	Author: Franz Regensburger
1274 ea0668a1c0ba added 8bit pragmas regensbu parents: diff changeset	3
17291 94f6113fe9ed converted to Isar theory format; wenzelm parents: 14981 diff changeset	4	Show that fix is the unique least fixed-point operator.
12036 49f6c49454c2 GPLed; wenzelm parents: 10835 diff changeset	5	From axioms gix1_def,gix2_def it follows that fix = gix
1274 ea0668a1c0ba added 8bit pragmas regensbu parents: diff changeset	6	*)
ea0668a1c0ba added 8bit pragmas regensbu parents: diff changeset	7
17291 94f6113fe9ed converted to Isar theory format; wenzelm parents: 14981 diff changeset	8	theory Fix2
94f6113fe9ed converted to Isar theory format; wenzelm parents: 14981 diff changeset	9	imports HOLCF
94f6113fe9ed converted to Isar theory format; wenzelm parents: 14981 diff changeset	10	begin
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25135 4f8176c940cf modernized specifications ('definition', 'axiomatization'); wenzelm parents: 19742 diff changeset	12	axiomatization
4f8176c940cf modernized specifications ('definition', 'axiomatization'); wenzelm parents: 19742 diff changeset	13	gix :: "('a->'a)->'a" where
4f8176c940cf modernized specifications ('definition', 'axiomatization'); wenzelm parents: 19742 diff changeset	14	gix1_def: "F$(gix$F) = gix$F" and
17291 94f6113fe9ed converted to Isar theory format; wenzelm parents: 14981 diff changeset	15	gix2_def: "F$y=y ==> gix$F << y"
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19742 86f21beabafc removed legacy ML scripts; wenzelm parents: 17291 diff changeset	17
86f21beabafc removed legacy ML scripts; wenzelm parents: 17291 diff changeset	18	lemma lemma1: "fix = gix"
86f21beabafc removed legacy ML scripts; wenzelm parents: 17291 diff changeset	19	apply (rule ext_cfun)
86f21beabafc removed legacy ML scripts; wenzelm parents: 17291 diff changeset	20	apply (rule antisym_less)
86f21beabafc removed legacy ML scripts; wenzelm parents: 17291 diff changeset	21	apply (rule fix_least)
86f21beabafc removed legacy ML scripts; wenzelm parents: 17291 diff changeset	22	apply (rule gix1_def)
86f21beabafc removed legacy ML scripts; wenzelm parents: 17291 diff changeset	23	apply (rule gix2_def)
86f21beabafc removed legacy ML scripts; wenzelm parents: 17291 diff changeset	24	apply (rule fix_eq [symmetric])
86f21beabafc removed legacy ML scripts; wenzelm parents: 17291 diff changeset	25	done
86f21beabafc removed legacy ML scripts; wenzelm parents: 17291 diff changeset	26
86f21beabafc removed legacy ML scripts; wenzelm parents: 17291 diff changeset	27	lemma lemma2: "gix$F=lub(range(%i. iterate i$F$UU))"
86f21beabafc removed legacy ML scripts; wenzelm parents: 17291 diff changeset	28	apply (rule lemma1 [THEN subst])
86f21beabafc removed legacy ML scripts; wenzelm parents: 17291 diff changeset	29	apply (rule fix_def2)
86f21beabafc removed legacy ML scripts; wenzelm parents: 17291 diff changeset	30	done
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ea0668a1c0ba added 8bit pragmas regensbu parents: diff changeset	32	end

author	haftmann
	Tue, 31 Aug 2010 13:15:35 +0200
changeset 38922	ec2a8efd8990
parent 35174	e15040ae75d7
child 40002	c5b5f7a3a3b1
permissions	-rw-r--r--