Definition df-uz 9463

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 9464 for its value, uzssz 9481 for its relationship to ZZ, nnuz 9497 and nn0uz 9496 for its relationships to NN and NN0, and eluz1 9466 and eluz2 9468 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 9462	. 2 class ZZ>=
2		vj	. . 3 setvar j
3		cz 9187	. . 3 class ZZ
4	2	cv 1342	. . . . 5 class j
5		vk	. . . . . 6 setvar k
6	5	cv 1342	. . . . 5 class k
7		cle 7930	. . . . 5 class <_
8	4, 6, 7	wbr 3981	. . . 4 wff j <_ k
9	8, 5, 3	crab 2447	. . 3 class { k e. ZZ | j <_ k }
10	2, 3, 9	cmpt 4042	. 2 class ( j e. ZZ |-> { k e. ZZ | j <_ k } )
11	1, 10	wceq 1343	1 wff ZZ>= = ( j e. ZZ |-> { k e. ZZ | j <_ k } )

This definition is referenced by:  uzval  9464  uzf  9465  uzennn  10367