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Definition df-uz 10227
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 10228 for its value, uzssz 10243 for its relationship to  ZZ, nnuz 10259 and nn0uz 10258 for its relationships to  NN and  NN0, and eluz1 10230 and eluz2 10232 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 10226 . 2  class  ZZ>=
2 vj . . 3  set  j
3 cz 10020 . . 3  class  ZZ
42cv 1623 . . . . 5  class  j
5 vk . . . . . 6  set  k
65cv 1623 . . . . 5  class  k
7 cle 8864 . . . . 5  class  <_
84, 6, 7wbr 4025 . . . 4  wff  j  <_ 
k
98, 5, 3crab 2549 . . 3  class  { k  e.  ZZ  |  j  <_  k }
102, 3, 9cmpt 4079 . 2  class  ( j  e.  ZZ  |->  { k  e.  ZZ  |  j  <_  k } )
111, 10wceq 1624 1  wff  ZZ>=  =  ( j  e.  ZZ  |->  { k  e.  ZZ  | 
j  <_  k }
)
Colors of variables: wff set class
This definition is referenced by:  uzval  10228  uzf  10229
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