Definition df-uz 12862

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 12863 for its value, uzssz 12882 for its relationship to ℤ, nnuz 12900 and nn0uz 12899 for its relationships to ℕ and ℕ₀, and eluz1 12865 and eluz2 12867 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 12861	. 2 class ℤ≥
2		vj	. . 3 setvar 𝑗
3		cz 12590	. . 3 class ℤ
4	2	cv 1567	. . . . 5 class 𝑗
5		vk	. . . . . 6 setvar 𝑘
6	5	cv 1567	. . . . 5 class 𝑘
7		cle 11243	. . . . 5 class ≤
8	4, 6, 7	wbr 5108	. . . 4 wff 𝑗 ≤ 𝑘
9	8, 5, 3	crab 3414	. . 3 class {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘}
10	2, 3, 9	cmpt 5191	. 2 class (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})
11	1, 10	wceq 1568	1 wff ℤ≥ = (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})

This definition is referenced by:  uzval  12863  uzf  12864