Definition df-uz 9564

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 9565 for its value, uzssz 9583 for its relationship to ZZ, nnuz 9599 and nn0uz 9598 for its relationships to NN and NN0, and eluz1 9567 and eluz2 9569 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 9563	. 2 class ZZ>=
2		vj	. . 3 setvar j
3		cz 9288	. . 3 class ZZ
4	2	cv 1363	. . . . 5 class j
5		vk	. . . . . 6 setvar k
6	5	cv 1363	. . . . 5 class k
7		cle 8028	. . . . 5 class <_
8	4, 6, 7	wbr 4021	. . . 4 wff j <_ k
9	8, 5, 3	crab 2472	. . 3 class { k e. ZZ | j <_ k }
10	2, 3, 9	cmpt 4082	. 2 class ( j e. ZZ |-> { k e. ZZ | j <_ k } )
11	1, 10	wceq 1364	1 wff ZZ>= = ( j e. ZZ |-> { k e. ZZ | j <_ k } )

This definition is referenced by:  uzval  9565  uzf  9566  uzennn  10473