Definition df-uz 12784

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 12785 for its value, uzssz 12804 for its relationship to ℤ, nnuz 12822 and nn0uz 12821 for its relationships to ℕ and ℕ₀, and eluz1 12787 and eluz2 12789 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 12783	. 2 class ℤ≥
2		vj	. . 3 setvar 𝑗
3		cz 12519	. . 3 class ℤ
4	2	cv 1547	. . . . 5 class 𝑗
5		vk	. . . . . 6 setvar 𝑘
6	5	cv 1547	. . . . 5 class 𝑘
7		cle 11176	. . . . 5 class ≤
8	4, 6, 7	wbr 5074	. . . 4 wff 𝑗 ≤ 𝑘
9	8, 5, 3	crab 3393	. . 3 class {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘}
10	2, 3, 9	cmpt 5155	. 2 class (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})
11	1, 10	wceq 1548	1 wff ℤ≥ = (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})

This definition is referenced by:  uzval  12785  uzf  12786