Definition df-uz 9756

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 9757 for its value, uzssz 9776 for its relationship to ℤ, nnuz 9792 and nn0uz 9791 for its relationships to ℕ and ℕ₀, and eluz1 9759 and eluz2 9761 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 9755	. 2 class ℤ≥
2		vj	. . 3 setvar 𝑗
3		cz 9479	. . 3 class ℤ
4	2	cv 1396	. . . . 5 class 𝑗
5		vk	. . . . . 6 setvar 𝑘
6	5	cv 1396	. . . . 5 class 𝑘
7		cle 8215	. . . . 5 class ≤
8	4, 6, 7	wbr 4088	. . . 4 wff 𝑗 ≤ 𝑘
9	8, 5, 3	crab 2514	. . 3 class {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘}
10	2, 3, 9	cmpt 4150	. 2 class (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})
11	1, 10	wceq 1397	1 wff ℤ≥ = (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})

This definition is referenced by:  uzval  9757  uzf  9758  uzennn  10699