Definition df-uz 9938

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 "ℤ_≥‘𝑀 " as "the set of integers greater than or equal to 𝑀". See uzval 9939 for its value, uzssz 9958 for its relationship to ℤ, nnuz 9974 and nn0uz 9973 for its relationships to ℕ and ℕ₀, and eluz1 9941 and eluz2 9943 for its membership relations. (Contributed by NM, 5-Sep-2005.)

Assertion

Ref	Expression
df-uz	⊢ ℤ≥ = (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})

Distinct variable group:   𝑗,𝑘

Detailed syntax breakdown of Definition df-uz

Step	Hyp	Ref	Expression
1		cuz 9937	. 2 class ℤ≥
2		vj	. . 3 setvar 𝑗
3		cz 9655	. . 3 class ℤ
4	2	cv 1401	. . . . 5 class 𝑗
5		vk	. . . . . 6 setvar 𝑘
6	5	cv 1401	. . . . 5 class 𝑘
7		cle 8367	. . . . 5 class ≤
8	4, 6, 7	wbr 4131	. . . 4 wff 𝑗 ≤ 𝑘
9	8, 5, 3	crab 2532	. . 3 class {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘}
10	2, 3, 9	cmpt 4193	. 2 class (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})
11	1, 10	wceq 1402	1 wff ℤ≥ = (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})

This definition is used by:  uzval  9939  uzf  9940  uzennn  10894