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Definition df-uz 10231
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 10232 for its value, uzssz 10247 for its relationship to  ZZ, nnuz 10263 and nn0uz 10262 for its relationships to  NN and  NN0, and eluz1 10234 and eluz2 10236 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 10230 . 2  class  ZZ>=
2 vj . . 3  set  j
3 cz 10024 . . 3  class  ZZ
42cv 1622 . . . . 5  class  j
5 vk . . . . . 6  set  k
65cv 1622 . . . . 5  class  k
7 cle 8868 . . . . 5  class  <_
84, 6, 7wbr 4023 . . . 4  wff  j  <_ 
k
98, 5, 3crab 2547 . . 3  class  { k  e.  ZZ  |  j  <_  k }
102, 3, 9cmpt 4077 . 2  class  ( j  e.  ZZ  |->  { k  e.  ZZ  |  j  <_  k } )
111, 10wceq 1623 1  wff  ZZ>=  =  ( j  e.  ZZ  |->  { k  e.  ZZ  | 
j  <_  k }
)
Colors of variables: wff set class
This definition is referenced by:  uzval  10232  uzf  10233
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