Definition df-uz 12904

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 12905 for its value, uzssz 12924 for its relationship to ℤ, nnuz 12946 and nn0uz 12945 for its relationships to ℕ and ℕ₀, and eluz1 12907 and eluz2 12909 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 12903	. 2 class ℤ≥
2		vj	. . 3 setvar 𝑗
3		cz 12639	. . 3 class ℤ
4	2	cv 1536	. . . . 5 class 𝑗
5		vk	. . . . . 6 setvar 𝑘
6	5	cv 1536	. . . . 5 class 𝑘
7		cle 11325	. . . . 5 class ≤
8	4, 6, 7	wbr 5166	. . . 4 wff 𝑗 ≤ 𝑘
9	8, 5, 3	crab 3443	. . 3 class {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘}
10	2, 3, 9	cmpt 5249	. 2 class (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})
11	1, 10	wceq 1537	1 wff ℤ≥ = (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})

This definition is referenced by:  uzval  12905  uzf  12906