Definition df-uz 12794

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 12795 for its value, uzssz 12814 for its relationship to ℤ, nnuz 12836 and nn0uz 12835 for its relationships to ℕ and ℕ₀, and eluz1 12797 and eluz2 12799 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 12793	. 2 class ℤ≥
2		vj	. . 3 setvar 𝑗
3		cz 12529	. . 3 class ℤ
4	2	cv 1539	. . . . 5 class 𝑗
5		vk	. . . . . 6 setvar 𝑘
6	5	cv 1539	. . . . 5 class 𝑘
7		cle 11209	. . . . 5 class ≤
8	4, 6, 7	wbr 5107	. . . 4 wff 𝑗 ≤ 𝑘
9	8, 5, 3	crab 3405	. . 3 class {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘}
10	2, 3, 9	cmpt 5188	. 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  12795  uzf  12796