Definition df-uz 12869

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 12870 for its value, uzssz 12889 for its relationship to ℤ, nnuz 12907 and nn0uz 12906 for its relationships to ℕ and ℕ₀, and eluz1 12872 and eluz2 12874 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 12868	. 2 class ℤ≥
2		vj	. . 3 setvar 𝑗
3		cz 12597	. . 3 class ℤ
4	2	cv 1568	. . . . 5 class 𝑗
5		vk	. . . . . 6 setvar 𝑘
6	5	cv 1568	. . . . 5 class 𝑘
7		cle 11250	. . . . 5 class ≤
8	4, 6, 7	wbr 5108	. . . 4 wff 𝑗 ≤ 𝑘
9	8, 5, 3	crab 3415	. . 3 class {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘}
10	2, 3, 9	cmpt 5191	. 2 class (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})
11	1, 10	wceq 1569	1 wff ℤ≥ = (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})

This definition is used by:  uzval  12870  uzf  12871