Definition df-uz 9467

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 9468 for its value, uzssz 9485 for its relationship to ℤ, nnuz 9501 and nn0uz 9500 for its relationships to ℕ and ℕ₀, and eluz1 9470 and eluz2 9472 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 9466	. 2 class ℤ≥
2		vj	. . 3 setvar 𝑗
3		cz 9191	. . 3 class ℤ
4	2	cv 1342	. . . . 5 class 𝑗
5		vk	. . . . . 6 setvar 𝑘
6	5	cv 1342	. . . . 5 class 𝑘
7		cle 7934	. . . . 5 class ≤
8	4, 6, 7	wbr 3982	. . . 4 wff 𝑗 ≤ 𝑘
9	8, 5, 3	crab 2448	. . 3 class {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘}
10	2, 3, 9	cmpt 4043	. 2 class (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})
11	1, 10	wceq 1343	1 wff ℤ≥ = (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})

This definition is referenced by:  uzval  9468  uzf  9469  uzennn  10371