Definition df-uz 8620

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 8621 for its value, uzssz 8638 for its relationship to ℤ, nnuz 8654 and nn0uz 8653 for its relationships to ℕ and ℕ₀, and eluz1 8623 and eluz2 8625 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 8619	. 2 class ℤ≥
2		vj	. . 3 setvar 𝑗
3		cz 8351	. . 3 class ℤ
4	2	cv 1283	. . . . 5 class 𝑗
5		vk	. . . . . 6 setvar 𝑘
6	5	cv 1283	. . . . 5 class 𝑘
7		cle 7154	. . . . 5 class ≤
8	4, 6, 7	wbr 3785	. . . 4 wff 𝑗 ≤ 𝑘
9	8, 5, 3	crab 2352	. . 3 class {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘}
10	2, 3, 9	cmpt 3839	. 2 class (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})
11	1, 10	wceq 1284	1 wff ℤ≥ = (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})

This definition is referenced by:  uzval  8621  uzf  8622