Definition df-uz 8952

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 8953 for its value, uzssz 8970 for its relationship to ZZ, nnuz 8986 and nn0uz 8985 for its relationships to NN and NN0, and eluz1 8955 and eluz2 8957 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 8951	. 2 class ZZ>=
2		vj	. . 3 setvar j
3		cz 8683	. . 3 class ZZ
4	2	cv 1286	. . . . 5 class j
5		vk	. . . . . 6 setvar k
6	5	cv 1286	. . . . 5 class k
7		cle 7467	. . . . 5 class <_
8	4, 6, 7	wbr 3820	. . . 4 wff j <_ k
9	8, 5, 3	crab 2359	. . 3 class { k e. ZZ | j <_ k }
10	2, 3, 9	cmpt 3874	. 2 class ( j e. ZZ |-> { k e. ZZ | j <_ k } )
11	1, 10	wceq 1287	1 wff ZZ>= = ( j e. ZZ |-> { k e. ZZ | j <_ k } )

This definition is referenced by:  uzval  8953  uzf  8954