Definition df-uz 9749

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 9750 for its value, uzssz 9769 for its relationship to ℤ, nnuz 9785 and nn0uz 9784 for its relationships to ℕ and ℕ₀, and eluz1 9752 and eluz2 9754 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 9748	. 2 class ℤ≥
2		vj	. . 3 setvar 𝑗
3		cz 9472	. . 3 class ℤ
4	2	cv 1394	. . . . 5 class 𝑗
5		vk	. . . . . 6 setvar 𝑘
6	5	cv 1394	. . . . 5 class 𝑘
7		cle 8208	. . . . 5 class ≤
8	4, 6, 7	wbr 4086	. . . 4 wff 𝑗 ≤ 𝑘
9	8, 5, 3	crab 2512	. . 3 class {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘}
10	2, 3, 9	cmpt 4148	. 2 class (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})
11	1, 10	wceq 1395	1 wff ℤ≥ = (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})

This definition is referenced by:  uzval  9750  uzf  9751  uzennn  10691