Definition df-uz 12730

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 12731 for its value, uzssz 12750 for its relationship to ℤ, nnuz 12772 and nn0uz 12771 for its relationships to ℕ and ℕ₀, and eluz1 12733 and eluz2 12735 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 12729	. 2 class ℤ≥
2		vj	. . 3 setvar 𝑗
3		cz 12465	. . 3 class ℤ
4	2	cv 1540	. . . . 5 class 𝑗
5		vk	. . . . . 6 setvar 𝑘
6	5	cv 1540	. . . . 5 class 𝑘
7		cle 11144	. . . . 5 class ≤
8	4, 6, 7	wbr 5091	. . . 4 wff 𝑗 ≤ 𝑘
9	8, 5, 3	crab 3395	. . 3 class {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘}
10	2, 3, 9	cmpt 5172	. 2 class (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})
11	1, 10	wceq 1541	1 wff ℤ≥ = (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})

This definition is referenced by:  uzval  12731  uzf  12732