Definition df-uz 8915

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 8916 for its value, uzssz 8933 for its relationship to ZZ, nnuz 8949 and nn0uz 8948 for its relationships to NN and NN0, and eluz1 8918 and eluz2 8920 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 8914	. 2 class ZZ>=
2		vj	. . 3 setvar j
3		cz 8646	. . 3 class ZZ
4	2	cv 1284	. . . . 5 class j
5		vk	. . . . . 6 setvar k
6	5	cv 1284	. . . . 5 class k
7		cle 7426	. . . . 5 class <_
8	4, 6, 7	wbr 3811	. . . 4 wff j <_ k
9	8, 5, 3	crab 2357	. . 3 class { k e. ZZ | j <_ k }
10	2, 3, 9	cmpt 3865	. 2 class ( j e. ZZ |-> { k e. ZZ | j <_ k } )
11	1, 10	wceq 1285	1 wff ZZ>= = ( j e. ZZ |-> { k e. ZZ | j <_ k } )

This definition is referenced by:  uzval  8916  uzf  8917