isabelle: src/HOL/NatDef.thy@33fe2d701ddd (annotated)

2608 450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	1	(* Title: HOL/NatDef.thy
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	2	ID: $Id$
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	3	Author: Tobias Nipkow, Cambridge University Computer Laboratory
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	4	Copyright 1991 University of Cambridge
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	5
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	6	Definition of types ind and nat.
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	7
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	8	Type nat is defined as a set Nat over type ind.
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	9	*)
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	10
10212 33fe2d701ddd * empty log message * nipkow parents: 8943 diff changeset	11	NatDef = Wellfounded_Recursion +
2608 450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	12
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	13	( type ind )
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	14
3947 eb707467f8c5 adapted to qualified names; wenzelm parents: 3842 diff changeset	15	global
eb707467f8c5 adapted to qualified names; wenzelm parents: 3842 diff changeset	16
2608 450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	17	types
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	18	ind
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	19
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	20	arities
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	21	ind :: term
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	22
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	23	consts
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	24	Zero_Rep :: ind
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	25	Suc_Rep :: ind => ind
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	26
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	27	rules
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	28	(the axiom of infinity in 2 parts)
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	29	inj_Suc_Rep "inj(Suc_Rep)"
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	30	Suc_Rep_not_Zero_Rep "Suc_Rep(x) ~= Zero_Rep"
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	31
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	32
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	33
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	34	( type nat )
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	35
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	36	(* type definition *)
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	37
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	38	typedef (Nat)
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	39	nat = "lfp(%X. {Zero_Rep} Un (Suc_Rep``X))" (lfp_def)
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	40
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	41	instance
8943 a4f8be72f585 now 0 is overloaded paulson parents: 7872 diff changeset	42	nat :: {ord, zero}
2608 450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	43
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	44
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	45	(* abstract constants and syntax *)
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	46
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	47	consts
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	48	Suc :: nat => nat
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	49	pred_nat :: "(nat * nat) set"
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	50
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	51	syntax
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	52	"1" :: nat ("1")
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	53	"2" :: nat ("2")
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	54
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	55	translations
5187 55f07169cf5f Removed nat_case, nat_rec, and natE (now provided by datatype berghofe parents: 3947 diff changeset	56	"1" == "Suc 0"
55f07169cf5f Removed nat_case, nat_rec, and natE (now provided by datatype berghofe parents: 3947 diff changeset	57	"2" == "Suc 1"
2608 450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	58
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	59
3947 eb707467f8c5 adapted to qualified names; wenzelm parents: 3842 diff changeset	60	local
eb707467f8c5 adapted to qualified names; wenzelm parents: 3842 diff changeset	61
2608 450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	62	defs
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	63	Zero_def "0 == Abs_Nat(Zero_Rep)"
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	64	Suc_def "Suc == (%n. Abs_Nat(Suc_Rep(Rep_Nat(n))))"
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	65
7872 2e2d7e80fb07 Removed obsolete comment. berghofe parents: 5187 diff changeset	66	(nat operations)
3236 882e125ed7da New pattern-matching definition of pred_nat paulson parents: 2608 diff changeset	67	pred_nat_def "pred_nat == {(m,n). n = Suc m}"
2608 450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	68
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	69	less_def "m<n == (m,n):trancl(pred_nat)"
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	70
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	71	le_def "m<=(n::nat) == ~(n<m)"
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	72
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	73	end

author	nipkow
	Thu, 12 Oct 2000 18:38:23 +0200
changeset 10212	33fe2d701ddd
parent 8943	a4f8be72f585
child 10832	e33b47e4246d
permissions	-rw-r--r--