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Definition df-uz 8569
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 8570 for its value, uzssz 8587 for its relationship to  ZZ, nnuz 8603 and nn0uz 8602 for its relationships to  NN and  NN0, and eluz1 8572 and eluz2 8574 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 8568 . 2  class  ZZ>=
2 vj . . 3  setvar  j
3 cz 8301 . . 3  class  ZZ
42cv 1258 . . . . 5  class  j
5 vk . . . . . 6  setvar  k
65cv 1258 . . . . 5  class  k
7 cle 7119 . . . . 5  class  <_
84, 6, 7wbr 3791 . . . 4  wff  j  <_ 
k
98, 5, 3crab 2327 . . 3  class  { k  e.  ZZ  |  j  <_  k }
102, 3, 9cmpt 3845 . 2  class  ( j  e.  ZZ  |->  { k  e.  ZZ  |  j  <_  k } )
111, 10wceq 1259 1  wff  ZZ>=  =  ( j  e.  ZZ  |->  { k  e.  ZZ  | 
j  <_  k }
)
Colors of variables: wff set class
This definition is referenced by:  uzval  8570  uzf  8571
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