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Definition df-uz 10481
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 10482 for its value, uzssz 10497 for its relationship to  ZZ, nnuz 10513 and nn0uz 10512 for its relationships to  NN and  NN0, and eluz1 10484 and eluz2 10486 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 10480 . 2  class  ZZ>=
2 vj . . 3  set  j
3 cz 10274 . . 3  class  ZZ
42cv 1651 . . . . 5  class  j
5 vk . . . . . 6  set  k
65cv 1651 . . . . 5  class  k
7 cle 9113 . . . . 5  class  <_
84, 6, 7wbr 4204 . . . 4  wff  j  <_ 
k
98, 5, 3crab 2701 . . 3  class  { k  e.  ZZ  |  j  <_  k }
102, 3, 9cmpt 4258 . 2  class  ( j  e.  ZZ  |->  { k  e.  ZZ  |  j  <_  k } )
111, 10wceq 1652 1  wff  ZZ>=  =  ( j  e.  ZZ  |->  { k  e.  ZZ  | 
j  <_  k }
)
Colors of variables: wff set class
This definition is referenced by:  uzval  10482  uzf  10483
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