Definition df-uz 12861

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 12862 for its value, uzssz 12881 for its relationship to ℤ, nnuz 12903 and nn0uz 12902 for its relationships to ℕ and ℕ₀, and eluz1 12864 and eluz2 12866 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 12860	. 2 class ℤ≥
2		vj	. . 3 setvar 𝑗
3		cz 12596	. . 3 class ℤ
4	2	cv 1538	. . . . 5 class 𝑗
5		vk	. . . . . 6 setvar 𝑘
6	5	cv 1538	. . . . 5 class 𝑘
7		cle 11278	. . . . 5 class ≤
8	4, 6, 7	wbr 5123	. . . 4 wff 𝑗 ≤ 𝑘
9	8, 5, 3	crab 3419	. . 3 class {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘}
10	2, 3, 9	cmpt 5205	. 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  12862  uzf  12863