Definition df-uz 12879

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 12880 for its value, uzssz 12899 for its relationship to ℤ, nnuz 12921 and nn0uz 12920 for its relationships to ℕ and ℕ₀, and eluz1 12882 and eluz2 12884 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 12878	. 2 class ℤ≥
2		vj	. . 3 setvar 𝑗
3		cz 12613	. . 3 class ℤ
4	2	cv 1539	. . . . 5 class 𝑗
5		vk	. . . . . 6 setvar 𝑘
6	5	cv 1539	. . . . 5 class 𝑘
7		cle 11296	. . . . 5 class ≤
8	4, 6, 7	wbr 5143	. . . 4 wff 𝑗 ≤ 𝑘
9	8, 5, 3	crab 3436	. . 3 class {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘}
10	2, 3, 9	cmpt 5225	. 2 class (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})
11	1, 10	wceq 1540	1 wff ℤ≥ = (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})

This definition is referenced by:  uzval  12880  uzf  12881