Definition df-uz 12739

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 12740 for its value, uzssz 12759 for its relationship to ℤ, nnuz 12777 and nn0uz 12776 for its relationships to ℕ and ℕ₀, and eluz1 12742 and eluz2 12744 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 12738	. 2 class ℤ≥
2		vj	. . 3 setvar 𝑗
3		cz 12475	. . 3 class ℤ
4	2	cv 1540	. . . . 5 class 𝑗
5		vk	. . . . . 6 setvar 𝑘
6	5	cv 1540	. . . . 5 class 𝑘
7		cle 11154	. . . . 5 class ≤
8	4, 6, 7	wbr 5093	. . . 4 wff 𝑗 ≤ 𝑘
9	8, 5, 3	crab 3396	. . 3 class {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘}
10	2, 3, 9	cmpt 5174	. 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  12740  uzf  12741