Definition df-uz 12820

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 12821 for its value, uzssz 12840 for its relationship to ℤ, nnuz 12862 and nn0uz 12861 for its relationships to ℕ and ℕ₀, and eluz1 12823 and eluz2 12825 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 12819	. 2 class ℤ≥
2		vj	. . 3 setvar 𝑗
3		cz 12555	. . 3 class ℤ
4	2	cv 1541	. . . . 5 class 𝑗
5		vk	. . . . . 6 setvar 𝑘
6	5	cv 1541	. . . . 5 class 𝑘
7		cle 11246	. . . . 5 class ≤
8	4, 6, 7	wbr 5148	. . . 4 wff 𝑗 ≤ 𝑘
9	8, 5, 3	crab 3433	. . 3 class {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘}
10	2, 3, 9	cmpt 5231	. 2 class (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})
11	1, 10	wceq 1542	1 wff ℤ≥ = (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})

This definition is referenced by:  uzval  12821  uzf  12822