Definition df-uz 9691

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 9692 for its value, uzssz 9710 for its relationship to ℤ, nnuz 9726 and nn0uz 9725 for its relationships to ℕ and ℕ₀, and eluz1 9694 and eluz2 9696 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 9690	. 2 class ℤ≥
2		vj	. . 3 setvar 𝑗
3		cz 9414	. . 3 class ℤ
4	2	cv 1374	. . . . 5 class 𝑗
5		vk	. . . . . 6 setvar 𝑘
6	5	cv 1374	. . . . 5 class 𝑘
7		cle 8150	. . . . 5 class ≤
8	4, 6, 7	wbr 4062	. . . 4 wff 𝑗 ≤ 𝑘
9	8, 5, 3	crab 2492	. . 3 class {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘}
10	2, 3, 9	cmpt 4124	. 2 class (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})
11	1, 10	wceq 1375	1 wff ℤ≥ = (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})

This definition is referenced by:  uzval  9692  uzf  9693  uzennn  10625