Definition df-uz 12583

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 12584 for its value, uzssz 12603 for its relationship to ℤ, nnuz 12621 and nn0uz 12620 for its relationships to ℕ and ℕ₀, and eluz1 12586 and eluz2 12588 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 12582	. 2 class ℤ≥
2		vj	. . 3 setvar 𝑗
3		cz 12319	. . 3 class ℤ
4	2	cv 1538	. . . . 5 class 𝑗
5		vk	. . . . . 6 setvar 𝑘
6	5	cv 1538	. . . . 5 class 𝑘
7		cle 11010	. . . . 5 class ≤
8	4, 6, 7	wbr 5074	. . . 4 wff 𝑗 ≤ 𝑘
9	8, 5, 3	crab 3068	. . 3 class {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘}
10	2, 3, 9	cmpt 5157	. 2 class (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})
11	1, 10	wceq 1539	1 wff ℤ≥ = (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})

This definition is referenced by:  uzval  12584  uzf  12585