Definition df-uz 12842

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 12843 for its value, uzssz 12862 for its relationship to ℤ, nnuz 12880 and nn0uz 12879 for its relationships to ℕ and ℕ₀, and eluz1 12845 and eluz2 12847 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 12841	. 2 class ℤ≥
2		vj	. . 3 setvar 𝑗
3		cz 12570	. . 3 class ℤ
4	2	cv 1561	. . . . 5 class 𝑗
5		vk	. . . . . 6 setvar 𝑘
6	5	cv 1561	. . . . 5 class 𝑘
7		cle 11219	. . . . 5 class ≤
8	4, 6, 7	wbr 5102	. . . 4 wff 𝑗 ≤ 𝑘
9	8, 5, 3	crab 3416	. . 3 class {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘}
10	2, 3, 9	cmpt 5183	. 2 class (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})
11	1, 10	wceq 1562	1 wff ℤ≥ = (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})

This definition is referenced by:  uzval  12843  uzf  12844