Definition df-uz 9739

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 9740 for its value, uzssz 9759 for its relationship to ℤ, nnuz 9775 and nn0uz 9774 for its relationships to ℕ and ℕ₀, and eluz1 9742 and eluz2 9744 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 9738	. 2 class ℤ≥
2		vj	. . 3 setvar 𝑗
3		cz 9462	. . 3 class ℤ
4	2	cv 1394	. . . . 5 class 𝑗
5		vk	. . . . . 6 setvar 𝑘
6	5	cv 1394	. . . . 5 class 𝑘
7		cle 8198	. . . . 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  9740  uzf  9741  uzennn  10675