Definition df-uz 12756

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 12757 for its value, uzssz 12776 for its relationship to ℤ, nnuz 12794 and nn0uz 12793 for its relationships to ℕ and ℕ₀, and eluz1 12759 and eluz2 12761 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 12755	. 2 class ℤ≥
2		vj	. . 3 setvar 𝑗
3		cz 12492	. . 3 class ℤ
4	2	cv 1541	. . . . 5 class 𝑗
5		vk	. . . . . 6 setvar 𝑘
6	5	cv 1541	. . . . 5 class 𝑘
7		cle 11171	. . . . 5 class ≤
8	4, 6, 7	wbr 5099	. . . 4 wff 𝑗 ≤ 𝑘
9	8, 5, 3	crab 3400	. . 3 class {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘}
10	2, 3, 9	cmpt 5180	. 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  12757  uzf  12758