Definition df-uz 9755

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 9756 for its value, uzssz 9775 for its relationship to ZZ, nnuz 9791 and nn0uz 9790 for its relationships to NN and NN0, and eluz1 9758 and eluz2 9760 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 9754	. 2 class ZZ>=
2		vj	. . 3 setvar j
3		cz 9478	. . 3 class ZZ
4	2	cv 1396	. . . . 5 class j
5		vk	. . . . . 6 setvar k
6	5	cv 1396	. . . . 5 class k
7		cle 8214	. . . . 5 class <_
8	4, 6, 7	wbr 4088	. . . 4 wff j <_ k
9	8, 5, 3	crab 2514	. . 3 class { k e. ZZ | j <_ k }
10	2, 3, 9	cmpt 4150	. 2 class ( j e. ZZ |-> { k e. ZZ | j <_ k } )
11	1, 10	wceq 1397	1 wff ZZ>= = ( j e. ZZ |-> { k e. ZZ | j <_ k } )

This definition is referenced by:  uzval  9756  uzf  9757  uzennn  10697