Definition df-uz 9327

Description: Define a function whose value at j is the semi-infinite set of contiguous integers starting at j, which we will also call the upper integers starting at j. Read " ZZ>= ` M " as "the set of integers greater than or equal to M." See uzval 9328 for its value, uzssz 9345 for its relationship to ZZ, nnuz 9361 and nn0uz 9360 for its relationships to NN and NN0, and eluz1 9330 and eluz2 9332 for its membership relations. (Contributed by NM, 5-Sep-2005.)

Assertion

Ref	Expression
df-uz	|- ZZ>= = ( j e. ZZ |-> { k e. ZZ | j <_ k } )

Distinct variable group:   j, k

Detailed syntax breakdown of Definition df-uz

Step	Hyp	Ref	Expression
1		cuz 9326	. 2 class ZZ>=
2		vj	. . 3 setvar j
3		cz 9054	. . 3 class ZZ
4	2	cv 1330	. . . . 5 class j
5		vk	. . . . . 6 setvar k
6	5	cv 1330	. . . . 5 class k
7		cle 7801	. . . . 5 class <_
8	4, 6, 7	wbr 3929	. . . 4 wff j <_ k
9	8, 5, 3	crab 2420	. . 3 class { k e. ZZ | j <_ k }
10	2, 3, 9	cmpt 3989	. 2 class ( j e. ZZ |-> { k e. ZZ | j <_ k } )
11	1, 10	wceq 1331	1 wff ZZ>= = ( j e. ZZ |-> { k e. ZZ | j <_ k } )

This definition is referenced by:  uzval  9328  uzf  9329  uzennn  10209