Definition df-uz 11564

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 11565 for its value, uzssz 11583 for its relationship to ℤ, nnuz 11599 and nn0uz 11598 for its relationships to ℕ and ℕ₀, and eluz1 11567 and eluz2 11569 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 11563	. 2 class ℤ≥
2		vj	. . 3 setvar 𝑗
3		cz 11254	. . 3 class ℤ
4	2	cv 1474	. . . . 5 class 𝑗
5		vk	. . . . . 6 setvar 𝑘
6	5	cv 1474	. . . . 5 class 𝑘
7		cle 9954	. . . . 5 class ≤
8	4, 6, 7	wbr 4583	. . . 4 wff 𝑗 ≤ 𝑘
9	8, 5, 3	crab 2900	. . 3 class {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘}
10	2, 3, 9	cmpt 4643	. 2 class (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})
11	1, 10	wceq 1475	1 wff ℤ≥ = (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})

This definition is referenced by:  uzval  11565  uzf  11566