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Definition df-uz 9564
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 9565 for its value, uzssz 9583 for its relationship to  ZZ, nnuz 9599 and nn0uz 9598 for its relationships to  NN and  NN0, and eluz1 9567 and eluz2 9569 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 9563 . 2  class  ZZ>=
2 vj . . 3  setvar  j
3 cz 9288 . . 3  class  ZZ
42cv 1363 . . . . 5  class  j
5 vk . . . . . 6  setvar  k
65cv 1363 . . . . 5  class  k
7 cle 8028 . . . . 5  class  <_
84, 6, 7wbr 4021 . . . 4  wff  j  <_ 
k
98, 5, 3crab 2472 . . 3  class  { k  e.  ZZ  |  j  <_  k }
102, 3, 9cmpt 4082 . 2  class  ( j  e.  ZZ  |->  { k  e.  ZZ  |  j  <_  k } )
111, 10wceq 1364 1  wff  ZZ>=  =  ( j  e.  ZZ  |->  { k  e.  ZZ  | 
j  <_  k }
)
Colors of variables: wff set class
This definition is referenced by:  uzval  9565  uzf  9566  uzennn  10473
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