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Definition df-uz 9339
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 9340 for its value, uzssz 9357 for its relationship to  ZZ, nnuz 9373 and nn0uz 9372 for its relationships to  NN and  NN0, and eluz1 9342 and eluz2 9344 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
StepHypRef Expression
1 cuz 9338 . 2  class  ZZ>=
2 vj . . 3  setvar  j
3 cz 9066 . . 3  class  ZZ
42cv 1330 . . . . 5  class  j
5 vk . . . . . 6  setvar  k
65cv 1330 . . . . 5  class  k
7 cle 7813 . . . . 5  class  <_
84, 6, 7wbr 3929 . . . 4  wff  j  <_ 
k
98, 5, 3crab 2420 . . 3  class  { k  e.  ZZ  |  j  <_  k }
102, 3, 9cmpt 3989 . 2  class  ( j  e.  ZZ  |->  { k  e.  ZZ  |  j  <_  k } )
111, 10wceq 1331 1  wff  ZZ>=  =  ( j  e.  ZZ  |->  { k  e.  ZZ  | 
j  <_  k }
)
Colors of variables: wff set class
This definition is referenced by:  uzval  9340  uzf  9341  uzennn  10221
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