Definition df-uz 9723

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 9724 for its value, uzssz 9742 for its relationship to ℤ, nnuz 9758 and nn0uz 9757 for its relationships to ℕ and ℕ₀, and eluz1 9726 and eluz2 9728 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 9722	. 2 class ℤ≥
2		vj	. . 3 setvar 𝑗
3		cz 9446	. . 3 class ℤ
4	2	cv 1394	. . . . 5 class 𝑗
5		vk	. . . . . 6 setvar 𝑘
6	5	cv 1394	. . . . 5 class 𝑘
7		cle 8182	. . . . 5 class ≤
8	4, 6, 7	wbr 4083	. . . 4 wff 𝑗 ≤ 𝑘
9	8, 5, 3	crab 2512	. . 3 class {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘}
10	2, 3, 9	cmpt 4145	. 2 class (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})
11	1, 10	wceq 1395	1 wff ℤ≥ = (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})

This definition is referenced by:  uzval  9724  uzf  9725  uzennn  10658