Definition df-uz 9320

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 9321 for its value, uzssz 9338 for its relationship to ZZ, nnuz 9354 and nn0uz 9353 for its relationships to NN and NN0, and eluz1 9323 and eluz2 9325 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 9319	. 2 class ZZ>=
2		vj	. . 3 setvar j
3		cz 9047	. . 3 class ZZ
4	2	cv 1330	. . . . 5 class j
5		vk	. . . . . 6 setvar k
6	5	cv 1330	. . . . 5 class k
7		cle 7794	. . . . 5 class <_
8	4, 6, 7	wbr 3924	. . . 4 wff j <_ k
9	8, 5, 3	crab 2418	. . 3 class { k e. ZZ | j <_ k }
10	2, 3, 9	cmpt 3984	. 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  9321  uzf  9322  uzennn  10202