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Definition df-uz 10320
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 10321 for its value, uzssz 10336 for its relationship to  ZZ, nnuz 10352 and nn0uz 10351 for its relationships to  NN and  NN0, and eluz1 10323 and eluz2 10325 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 10319 . 2  class  ZZ>=
2 vj . . 3  set  j
3 cz 10113 . . 3  class  ZZ
42cv 1641 . . . . 5  class  j
5 vk . . . . . 6  set  k
65cv 1641 . . . . 5  class  k
7 cle 8955 . . . . 5  class  <_
84, 6, 7wbr 4102 . . . 4  wff  j  <_ 
k
98, 5, 3crab 2623 . . 3  class  { k  e.  ZZ  |  j  <_  k }
102, 3, 9cmpt 4156 . 2  class  ( j  e.  ZZ  |->  { k  e.  ZZ  |  j  <_  k } )
111, 10wceq 1642 1  wff  ZZ>=  =  ( j  e.  ZZ  |->  { k  e.  ZZ  | 
j  <_  k }
)
Colors of variables: wff set class
This definition is referenced by:  uzval  10321  uzf  10322
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