Definition df-uz 12851

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 12852 for its value, uzssz 12871 for its relationship to ℤ, nnuz 12893 and nn0uz 12892 for its relationships to ℕ and ℕ₀, and eluz1 12854 and eluz2 12856 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 12850	. 2 class ℤ≥
2		vj	. . 3 setvar 𝑗
3		cz 12586	. . 3 class ℤ
4	2	cv 1539	. . . . 5 class 𝑗
5		vk	. . . . . 6 setvar 𝑘
6	5	cv 1539	. . . . 5 class 𝑘
7		cle 11268	. . . . 5 class ≤
8	4, 6, 7	wbr 5119	. . . 4 wff 𝑗 ≤ 𝑘
9	8, 5, 3	crab 3415	. . 3 class {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘}
10	2, 3, 9	cmpt 5201	. 2 class (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})
11	1, 10	wceq 1540	1 wff ℤ≥ = (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})

This definition is referenced by:  uzval  12852  uzf  12853