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Definition df-uz 8250
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 8251 for its value, uzssz 8268 for its relationship to  ZZ, nnuz 8284 and nn0uz 8283 for its relationships to  NN and  NN0, and eluz1 8253 and eluz2 8255 for its membership relations. (Contributed by NM, 5-Sep-2005.)
Assertion
Ref Expression
df-uz  ZZ>=  j  ZZ  |->  { k  ZZ  | 
j  <_  k }
Distinct variable group:    j, k

Detailed syntax breakdown of Definition df-uz
StepHypRef Expression
1 cuz 8249 . 2  ZZ>=
2 vj . . 3  setvar  j
3 cz 8021 . . 3  ZZ
42cv 1241 . . . . 5  j
5 vk . . . . . 6  setvar  k
65cv 1241 . . . . 5  k
7 cle 6858 . . . . 5  <_
84, 6, 7wbr 3755 . . . 4  j  <_  k
98, 5, 3crab 2304 . . 3  { k  ZZ  |  j  <_  k }
102, 3, 9cmpt 3809 . 2  j  ZZ  |->  { k  ZZ  |  j  <_  k }
111, 10wceq 1242 1  ZZ>=  j  ZZ  |->  { k  ZZ  | 
j  <_  k }
Colors of variables: wff set class
This definition is referenced by:  uzval  8251  uzf  8252
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