Definition df-uz 9656

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 9657 for its value, uzssz 9675 for its relationship to ℤ, nnuz 9691 and nn0uz 9690 for its relationships to ℕ and ℕ₀, and eluz1 9659 and eluz2 9661 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 9655	. 2 class ℤ≥
2		vj	. . 3 setvar 𝑗
3		cz 9379	. . 3 class ℤ
4	2	cv 1372	. . . . 5 class 𝑗
5		vk	. . . . . 6 setvar 𝑘
6	5	cv 1372	. . . . 5 class 𝑘
7		cle 8115	. . . . 5 class ≤
8	4, 6, 7	wbr 4047	. . . 4 wff 𝑗 ≤ 𝑘
9	8, 5, 3	crab 2489	. . 3 class {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘}
10	2, 3, 9	cmpt 4109	. 2 class (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})
11	1, 10	wceq 1373	1 wff ℤ≥ = (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})

This definition is referenced by:  uzval  9657  uzf  9658  uzennn  10588