Definition df-uz 12822

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 12823 for its value, uzssz 12842 for its relationship to ℤ, nnuz 12864 and nn0uz 12863 for its relationships to ℕ and ℕ₀, and eluz1 12825 and eluz2 12827 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 12821	. 2 class ℤ≥
2		vj	. . 3 setvar 𝑗
3		cz 12557	. . 3 class ℤ
4	2	cv 1532	. . . . 5 class 𝑗
5		vk	. . . . . 6 setvar 𝑘
6	5	cv 1532	. . . . 5 class 𝑘
7		cle 11248	. . . . 5 class ≤
8	4, 6, 7	wbr 5139	. . . 4 wff 𝑗 ≤ 𝑘
9	8, 5, 3	crab 3424	. . 3 class {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘}
10	2, 3, 9	cmpt 5222	. 2 class (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})
11	1, 10	wceq 1533	1 wff ℤ≥ = (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})

This definition is referenced by:  uzval  12823  uzf  12824