Definition df-uz 9351

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 9352 for its value, uzssz 9369 for its relationship to ZZ, nnuz 9385 and nn0uz 9384 for its relationships to NN and NN0, and eluz1 9354 and eluz2 9356 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 9350	. 2 class ZZ>=
2		vj	. . 3 setvar j
3		cz 9078	. . 3 class ZZ
4	2	cv 1331	. . . . 5 class j
5		vk	. . . . . 6 setvar k
6	5	cv 1331	. . . . 5 class k
7		cle 7825	. . . . 5 class <_
8	4, 6, 7	wbr 3937	. . . 4 wff j <_ k
9	8, 5, 3	crab 2421	. . 3 class { k e. ZZ | j <_ k }
10	2, 3, 9	cmpt 3997	. 2 class ( j e. ZZ |-> { k e. ZZ | j <_ k } )
11	1, 10	wceq 1332	1 wff ZZ>= = ( j e. ZZ |-> { k e. ZZ | j <_ k } )

This definition is referenced by:  uzval  9352  uzf  9353  uzennn  10240