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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 "𝑀 " as "the set of integers greater than or equal to 𝑀." See uzval 8953 for its value, uzssz 8970 for its relationship to , nnuz 8986 and nn0uz 8985 for its relationships to and 0, and eluz1 8955 and eluz2 8957 for its membership relations. (Contributed by NM, 5-Sep-2005.)
Assertion
Ref Expression
df-uz = (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗𝑘})
Distinct variable group:   𝑗,𝑘

Detailed syntax breakdown of Definition df-uz
StepHypRef Expression
1 cuz 8951 . 2 class
2 vj . . 3 setvar 𝑗
3 cz 8683 . . 3 class
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 𝑗𝑘
98, 5, 3crab 2359 . . 3 class {𝑘 ∈ ℤ ∣ 𝑗𝑘}
102, 3, 9cmpt 3874 . 2 class (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗𝑘})
111, 10wceq 1287 1 wff = (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗𝑘})
Colors of variables: wff set class
This definition is referenced by:  uzval  8953  uzf  8954
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