Definition df-uz 9596

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 9597 for its value, uzssz 9615 for its relationship to ℤ, nnuz 9631 and nn0uz 9630 for its relationships to ℕ and ℕ₀, and eluz1 9599 and eluz2 9601 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 9595	. 2 class ℤ≥
2		vj	. . 3 setvar 𝑗
3		cz 9320	. . 3 class ℤ
4	2	cv 1363	. . . . 5 class 𝑗
5		vk	. . . . . 6 setvar 𝑘
6	5	cv 1363	. . . . 5 class 𝑘
7		cle 8057	. . . . 5 class ≤
8	4, 6, 7	wbr 4030	. . . 4 wff 𝑗 ≤ 𝑘
9	8, 5, 3	crab 2476	. . 3 class {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘}
10	2, 3, 9	cmpt 4091	. 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  9597  uzf  9598  uzennn  10510