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Definition df-uz 10445
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 10446 for its value, uzssz 10461 for its relationship to  ZZ, nnuz 10477 and nn0uz 10476 for its relationships to  NN and  NN0, and eluz1 10448 and eluz2 10450 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 10444 . 2  class  ZZ>=
2 vj . . 3  set  j
3 cz 10238 . . 3  class  ZZ
42cv 1648 . . . . 5  class  j
5 vk . . . . . 6  set  k
65cv 1648 . . . . 5  class  k
7 cle 9077 . . . . 5  class  <_
84, 6, 7wbr 4172 . . . 4  wff  j  <_ 
k
98, 5, 3crab 2670 . . 3  class  { k  e.  ZZ  |  j  <_  k }
102, 3, 9cmpt 4226 . 2  class  ( j  e.  ZZ  |->  { k  e.  ZZ  |  j  <_  k } )
111, 10wceq 1649 1  wff  ZZ>=  =  ( j  e.  ZZ  |->  { k  e.  ZZ  | 
j  <_  k }
)
Colors of variables: wff set class
This definition is referenced by:  uzval  10446  uzf  10447
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