Definition df-uz 9731

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 9732 for its value, uzssz 9750 for its relationship to ℤ, nnuz 9766 and nn0uz 9765 for its relationships to ℕ and ℕ₀, and eluz1 9734 and eluz2 9736 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 9730	. 2 class ℤ≥
2		vj	. . 3 setvar 𝑗
3		cz 9454	. . 3 class ℤ
4	2	cv 1394	. . . . 5 class 𝑗
5		vk	. . . . . 6 setvar 𝑘
6	5	cv 1394	. . . . 5 class 𝑘
7		cle 8190	. . . . 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  9732  uzf  9733  uzennn  10666