Definition df-uz 12753

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 12754 for its value, uzssz 12773 for its relationship to ℤ, nnuz 12791 and nn0uz 12790 for its relationships to ℕ and ℕ₀, and eluz1 12756 and eluz2 12758 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 12752	. 2 class ℤ≥
2		vj	. . 3 setvar 𝑗
3		cz 12489	. . 3 class ℤ
4	2	cv 1541	. . . . 5 class 𝑗
5		vk	. . . . . 6 setvar 𝑘
6	5	cv 1541	. . . . 5 class 𝑘
7		cle 11168	. . . . 5 class ≤
8	4, 6, 7	wbr 5086	. . . 4 wff 𝑗 ≤ 𝑘
9	8, 5, 3	crab 3390	. . 3 class {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘}
10	2, 3, 9	cmpt 5167	. 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  12754  uzf  12755