Definition df-uz 9854

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 9855 for its value, uzssz 9874 for its relationship to ZZ, nnuz 9890 and nn0uz 9889 for its relationships to NN and NN0, and eluz1 9857 and eluz2 9859 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 9853	. 2 class ZZ>=
2		vj	. . 3 setvar j
3		cz 9577	. . 3 class ZZ
4	2	cv 1397	. . . . 5 class j
5		vk	. . . . . 6 setvar k
6	5	cv 1397	. . . . 5 class k
7		cle 8309	. . . . 5 class <_
8	4, 6, 7	wbr 4109	. . . 4 wff j <_ k
9	8, 5, 3	crab 2524	. . 3 class { k e. ZZ | j <_ k }
10	2, 3, 9	cmpt 4171	. 2 class ( j e. ZZ |-> { k e. ZZ | j <_ k } )
11	1, 10	wceq 1398	1 wff ZZ>= = ( j e. ZZ |-> { k e. ZZ | j <_ k } )

This definition is referenced by:  uzval  9855  uzf  9856  uzennn  10798