Definition df-uz 8474

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 8475 for its value, uzssz 8492 for its relationship to ZZ, nnuz 8508 and nn0uz 8507 for its relationships to NN and NN0, and eluz1 8477 and eluz2 8479 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 8473	. 2 class ZZ>=
2		vj	. . 3 setvar j
3		cz 8245	. . 3 class ZZ
4	2	cv 1242	. . . . 5 class j
5		vk	. . . . . 6 setvar k
6	5	cv 1242	. . . . 5 class k
7		cle 7061	. . . . 5 class <_
8	4, 6, 7	wbr 3764	. . . 4 wff j <_ k
9	8, 5, 3	crab 2310	. . 3 class { k e. ZZ | j <_ k }
10	2, 3, 9	cmpt 3818	. 2 class ( j e. ZZ |-> { k e. ZZ | j <_ k } )
11	1, 10	wceq 1243	1 wff ZZ>= = ( j e. ZZ |-> { k e. ZZ | j <_ k } )

This definition is referenced by:  uzval  8475  uzf  8476