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Definition df-uz 9177
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 9178 for its value, uzssz 9195 for its relationship to  ZZ, nnuz 9211 and nn0uz 9210 for its relationships to  NN and  NN0, and eluz1 9180 and eluz2 9182 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 9176 . 2  class  ZZ>=
2 vj . . 3  setvar  j
3 cz 8906 . . 3  class  ZZ
42cv 1298 . . . . 5  class  j
5 vk . . . . . 6  setvar  k
65cv 1298 . . . . 5  class  k
7 cle 7673 . . . . 5  class  <_
84, 6, 7wbr 3875 . . . 4  wff  j  <_ 
k
98, 5, 3crab 2379 . . 3  class  { k  e.  ZZ  |  j  <_  k }
102, 3, 9cmpt 3929 . 2  class  ( j  e.  ZZ  |->  { k  e.  ZZ  |  j  <_  k } )
111, 10wceq 1299 1  wff  ZZ>=  =  ( j  e.  ZZ  |->  { k  e.  ZZ  | 
j  <_  k }
)
Colors of variables: wff set class
This definition is referenced by:  uzval  9178  uzf  9179  uzennn  10050
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