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Definition df-uz 9283
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 9284 for its value, uzssz 9301 for its relationship to  ZZ, nnuz 9317 and nn0uz 9316 for its relationships to  NN and  NN0, and eluz1 9286 and eluz2 9288 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 9282 . 2  class  ZZ>=
2 vj . . 3  setvar  j
3 cz 9012 . . 3  class  ZZ
42cv 1315 . . . . 5  class  j
5 vk . . . . . 6  setvar  k
65cv 1315 . . . . 5  class  k
7 cle 7769 . . . . 5  class  <_
84, 6, 7wbr 3899 . . . 4  wff  j  <_ 
k
98, 5, 3crab 2397 . . 3  class  { k  e.  ZZ  |  j  <_  k }
102, 3, 9cmpt 3959 . 2  class  ( j  e.  ZZ  |->  { k  e.  ZZ  |  j  <_  k } )
111, 10wceq 1316 1  wff  ZZ>=  =  ( j  e.  ZZ  |->  { k  e.  ZZ  | 
j  <_  k }
)
Colors of variables: wff set class
This definition is referenced by:  uzval  9284  uzf  9285  uzennn  10164
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