Definition df-uz 9931

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 9932 for its value, uzssz 9951 for its relationship to ZZ, nnuz 9967 and nn0uz 9966 for its relationships to NN and NN0, and eluz1 9934 and eluz2 9936 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 9930	. 2 class ZZ>=
2		vj	. . 3 setvar j
3		cz 9648	. . 3 class ZZ
4	2	cv 1401	. . . . 5 class j
5		vk	. . . . . 6 setvar k
6	5	cv 1401	. . . . 5 class k
7		cle 8361	. . . . 5 class <_
8	4, 6, 7	wbr 4130	. . . 4 wff j <_ k
9	8, 5, 3	crab 2532	. . 3 class { k e. ZZ | j <_ k }
10	2, 3, 9	cmpt 4192	. 2 class ( j e. ZZ |-> { k e. ZZ | j <_ k } )
11	1, 10	wceq 1402	1 wff ZZ>= = ( j e. ZZ |-> { k e. ZZ | j <_ k } )

This definition is used by:  uzval  9932  uzf  9933  uzennn  10886