isabelle: src/HOL/NatDef.thy@1d5d181b7e28 (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
11326 680ebd093cfe Representing set for type nat is now defined via "inductive". berghofe parents: 10832 diff changeset	38	consts
680ebd093cfe Representing set for type nat is now defined via "inductive". berghofe parents: 10832 diff changeset	39	Nat' :: "ind set"
680ebd093cfe Representing set for type nat is now defined via "inductive". berghofe parents: 10832 diff changeset	40
680ebd093cfe Representing set for type nat is now defined via "inductive". berghofe parents: 10832 diff changeset	41	inductive Nat'
680ebd093cfe Representing set for type nat is now defined via "inductive". berghofe parents: 10832 diff changeset	42	intrs
680ebd093cfe Representing set for type nat is now defined via "inductive". berghofe parents: 10832 diff changeset	43	Zero_RepI "Zero_Rep : Nat'"
680ebd093cfe Representing set for type nat is now defined via "inductive". berghofe parents: 10832 diff changeset	44	Suc_RepI "i : Nat' ==> Suc_Rep i : Nat'"
680ebd093cfe Representing set for type nat is now defined via "inductive". berghofe parents: 10832 diff changeset	45
2608 450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	46	typedef (Nat)
11326 680ebd093cfe Representing set for type nat is now defined via "inductive". berghofe parents: 10832 diff changeset	47	nat = "Nat'" (Nat'.Zero_RepI)
2608 450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	48
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	49	instance
8943 a4f8be72f585 now 0 is overloaded paulson parents: 7872 diff changeset	50	nat :: {ord, zero}
2608 450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	51
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	52
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	53	(* abstract constants and syntax *)
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	54
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	55	consts
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	56	Suc :: nat => nat
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	57	pred_nat :: "(nat * nat) set"
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	58
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	59	syntax
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	60	"1" :: nat ("1")
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	61	"2" :: nat ("2")
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	62
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	63	translations
5187 55f07169cf5f Removed nat_case, nat_rec, and natE (now provided by datatype berghofe parents: 3947 diff changeset	64	"1" == "Suc 0"
55f07169cf5f Removed nat_case, nat_rec, and natE (now provided by datatype berghofe parents: 3947 diff changeset	65	"2" == "Suc 1"
2608 450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	66
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	67
3947 eb707467f8c5 adapted to qualified names; wenzelm parents: 3842 diff changeset	68	local
eb707467f8c5 adapted to qualified names; wenzelm parents: 3842 diff changeset	69
2608 450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	70	defs
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	71	Zero_def "0 == Abs_Nat(Zero_Rep)"
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	72	Suc_def "Suc == (%n. Abs_Nat(Suc_Rep(Rep_Nat(n))))"
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	73
7872 2e2d7e80fb07 Removed obsolete comment. berghofe parents: 5187 diff changeset	74	(nat operations)
3236 882e125ed7da New pattern-matching definition of pred_nat paulson parents: 2608 diff changeset	75	pred_nat_def "pred_nat == {(m,n). n = Suc m}"
2608 450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	76
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	77	less_def "m<n == (m,n):trancl(pred_nat)"
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	78
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	79	le_def "m<=(n::nat) == ~(n<m)"
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	80
450c9b682a92 New class "order" and accompanying changes. nipkow parents: diff changeset	81	end

author	berghofe
	Mon, 11 Jun 2001 19:21:13 +0200
changeset 11371	1d5d181b7e28
parent 11326	680ebd093cfe
child 11464	ddea204de5bc
permissions	-rw-r--r--