Definition df-uz 9734

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 9735 for its value, uzssz 9754 for its relationship to ZZ, nnuz 9770 and nn0uz 9769 for its relationships to NN and NN0, and eluz1 9737 and eluz2 9739 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 9733	. 2 class ZZ>=
2		vj	. . 3 setvar j
3		cz 9457	. . 3 class ZZ
4	2	cv 1394	. . . . 5 class j
5		vk	. . . . . 6 setvar k
6	5	cv 1394	. . . . 5 class k
7		cle 8193	. . . . 5 class <_
8	4, 6, 7	wbr 4083	. . . 4 wff j <_ k
9	8, 5, 3	crab 2512	. . 3 class { k e. ZZ | j <_ k }
10	2, 3, 9	cmpt 4145	. 2 class ( j e. ZZ |-> { k e. ZZ | j <_ k } )
11	1, 10	wceq 1395	1 wff ZZ>= = ( j e. ZZ |-> { k e. ZZ | j <_ k } )

This definition is referenced by:  uzval  9735  uzf  9736  uzennn  10670