Definition df-uz 9602

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 9603 for its value, uzssz 9621 for its relationship to ℤ, nnuz 9637 and nn0uz 9636 for its relationships to ℕ and ℕ₀, and eluz1 9605 and eluz2 9607 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 9601	. 2 class ℤ≥
2		vj	. . 3 setvar 𝑗
3		cz 9326	. . 3 class ℤ
4	2	cv 1363	. . . . 5 class 𝑗
5		vk	. . . . . 6 setvar 𝑘
6	5	cv 1363	. . . . 5 class 𝑘
7		cle 8062	. . . . 5 class ≤
8	4, 6, 7	wbr 4033	. . . 4 wff 𝑗 ≤ 𝑘
9	8, 5, 3	crab 2479	. . 3 class {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘}
10	2, 3, 9	cmpt 4094	. 2 class (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})
11	1, 10	wceq 1364	1 wff ℤ≥ = (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})

This definition is referenced by:  uzval  9603  uzf  9604  uzennn  10528