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Definition df-uz 10494
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 10495 for its value, uzssz 10510 for its relationship to  ZZ, nnuz 10526 and nn0uz 10525 for its relationships to  NN and  NN0, and eluz1 10497 and eluz2 10499 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 10493 . 2  class  ZZ>=
2 vj . . 3  set  j
3 cz 10287 . . 3  class  ZZ
42cv 1652 . . . . 5  class  j
5 vk . . . . . 6  set  k
65cv 1652 . . . . 5  class  k
7 cle 9126 . . . . 5  class  <_
84, 6, 7wbr 4215 . . . 4  wff  j  <_ 
k
98, 5, 3crab 2711 . . 3  class  { k  e.  ZZ  |  j  <_  k }
102, 3, 9cmpt 4269 . 2  class  ( j  e.  ZZ  |->  { k  e.  ZZ  |  j  <_  k } )
111, 10wceq 1653 1  wff  ZZ>=  =  ( j  e.  ZZ  |->  { k  e.  ZZ  | 
j  <_  k }
)
Colors of variables: wff set class
This definition is referenced by:  uzval  10495  uzf  10496
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