Definition df-uz 9648

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 9649 for its value, uzssz 9667 for its relationship to ZZ, nnuz 9683 and nn0uz 9682 for its relationships to NN and NN0, and eluz1 9651 and eluz2 9653 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 9647	. 2 class ZZ>=
2		vj	. . 3 setvar j
3		cz 9371	. . 3 class ZZ
4	2	cv 1371	. . . . 5 class j
5		vk	. . . . . 6 setvar k
6	5	cv 1371	. . . . 5 class k
7		cle 8107	. . . . 5 class <_
8	4, 6, 7	wbr 4043	. . . 4 wff j <_ k
9	8, 5, 3	crab 2487	. . 3 class { k e. ZZ | j <_ k }
10	2, 3, 9	cmpt 4104	. 2 class ( j e. ZZ |-> { k e. ZZ | j <_ k } )
11	1, 10	wceq 1372	1 wff ZZ>= = ( j e. ZZ |-> { k e. ZZ | j <_ k } )

This definition is referenced by:  uzval  9649  uzf  9650  uzennn  10579