Definition df-uz 9475

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 9476 for its value, uzssz 9493 for its relationship to ZZ, nnuz 9509 and nn0uz 9508 for its relationships to NN and NN0, and eluz1 9478 and eluz2 9480 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 9474	. 2 class ZZ>=
2		vj	. . 3 setvar j
3		cz 9199	. . 3 class ZZ
4	2	cv 1347	. . . . 5 class j
5		vk	. . . . . 6 setvar k
6	5	cv 1347	. . . . 5 class k
7		cle 7942	. . . . 5 class <_
8	4, 6, 7	wbr 3987	. . . 4 wff j <_ k
9	8, 5, 3	crab 2452	. . 3 class { k e. ZZ | j <_ k }
10	2, 3, 9	cmpt 4048	. 2 class ( j e. ZZ |-> { k e. ZZ | j <_ k } )
11	1, 10	wceq 1348	1 wff ZZ>= = ( j e. ZZ |-> { k e. ZZ | j <_ k } )

This definition is referenced by:  uzval  9476  uzf  9477  uzennn  10379