Definition df-uz 9593

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 9594 for its value, uzssz 9612 for its relationship to ℤ, nnuz 9628 and nn0uz 9627 for its relationships to ℕ and ℕ₀, and eluz1 9596 and eluz2 9598 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 9592	. 2 class ℤ≥
2		vj	. . 3 setvar 𝑗
3		cz 9317	. . 3 class ℤ
4	2	cv 1363	. . . . 5 class 𝑗
5		vk	. . . . . 6 setvar 𝑘
6	5	cv 1363	. . . . 5 class 𝑘
7		cle 8055	. . . . 5 class ≤
8	4, 6, 7	wbr 4029	. . . 4 wff 𝑗 ≤ 𝑘
9	8, 5, 3	crab 2476	. . 3 class {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘}
10	2, 3, 9	cmpt 4090	. 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  9594  uzf  9595  uzennn  10507