Definition df-uz 11688

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 11689 for its value, uzssz 11707 for its relationship to ZZ, nnuz 11723 and nn0uz 11722 for its relationships to NN and NN0, and eluz1 11691 and eluz2 11693 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 11687	. 2 class ZZ>=
2		vj	. . 3 setvar j
3		cz 11377	. . 3 class ZZ
4	2	cv 1482	. . . . 5 class j
5		vk	. . . . . 6 setvar k
6	5	cv 1482	. . . . 5 class k
7		cle 10075	. . . . 5 class <_
8	4, 6, 7	wbr 4653	. . . 4 wff j <_ k
9	8, 5, 3	crab 2916	. . 3 class { k e. ZZ | j <_ k }
10	2, 3, 9	cmpt 4729	. 2 class ( j e. ZZ |-> { k e. ZZ | j <_ k } )
11	1, 10	wceq 1483	1 wff ZZ>= = ( j e. ZZ |-> { k e. ZZ | j <_ k } )

This definition is referenced by:  uzval  11689  uzf  11690