Definition df-uz 9857

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 9858 for its value, uzssz 9877 for its relationship to ZZ, nnuz 9893 and nn0uz 9892 for its relationships to NN and NN0, and eluz1 9860 and eluz2 9862 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 9856	. 2 class ZZ>=
2		vj	. . 3 setvar j
3		cz 9579	. . 3 class ZZ
4	2	cv 1397	. . . . 5 class j
5		vk	. . . . . 6 setvar k
6	5	cv 1397	. . . . 5 class k
7		cle 8311	. . . . 5 class <_
8	4, 6, 7	wbr 4111	. . . 4 wff j <_ k
9	8, 5, 3	crab 2526	. . 3 class { k e. ZZ | j <_ k }
10	2, 3, 9	cmpt 4173	. 2 class ( j e. ZZ |-> { k e. ZZ | j <_ k } )
11	1, 10	wceq 1398	1 wff ZZ>= = ( j e. ZZ |-> { k e. ZZ | j <_ k } )

This definition is referenced by:  uzval  9858  uzf  9859  uzennn  10802