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Definition df-uz 8952
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 8953 for its value, uzssz 8970 for its relationship to  ZZ, nnuz 8986 and nn0uz 8985 for its relationships to  NN and  NN0, and eluz1 8955 and eluz2 8957 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 8951 . 2  class  ZZ>=
2 vj . . 3  setvar  j
3 cz 8683 . . 3  class  ZZ
42cv 1286 . . . . 5  class  j
5 vk . . . . . 6  setvar  k
65cv 1286 . . . . 5  class  k
7 cle 7467 . . . . 5  class  <_
84, 6, 7wbr 3820 . . . 4  wff  j  <_ 
k
98, 5, 3crab 2359 . . 3  class  { k  e.  ZZ  |  j  <_  k }
102, 3, 9cmpt 3874 . 2  class  ( j  e.  ZZ  |->  { k  e.  ZZ  |  j  <_  k } )
111, 10wceq 1287 1  wff  ZZ>=  =  ( j  e.  ZZ  |->  { k  e.  ZZ  | 
j  <_  k }
)
Colors of variables: wff set class
This definition is referenced by:  uzval  8953  uzf  8954
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