Definition df-uz 9922

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 9923 for its value, uzssz 9942 for its relationship to ZZ, nnuz 9958 and nn0uz 9957 for its relationships to NN and NN0, and eluz1 9925 and eluz2 9927 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 9921	. 2 class ZZ>=
2		vj	. . 3 setvar j
3		cz 9644	. . 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  9923  uzf  9924  uzennn  10873