Definition df-uz 12853

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 12854 for its value, uzssz 12873 for its relationship to ℤ, nnuz 12895 and nn0uz 12894 for its relationships to ℕ and ℕ₀, and eluz1 12856 and eluz2 12858 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 12852	. 2 class ℤ≥
2		vj	. . 3 setvar 𝑗
3		cz 12588	. . 3 class ℤ
4	2	cv 1533	. . . . 5 class 𝑗
5		vk	. . . . . 6 setvar 𝑘
6	5	cv 1533	. . . . 5 class 𝑘
7		cle 11279	. . . . 5 class ≤
8	4, 6, 7	wbr 5148	. . . 4 wff 𝑗 ≤ 𝑘
9	8, 5, 3	crab 3429	. . 3 class {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘}
10	2, 3, 9	cmpt 5231	. 2 class (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})
11	1, 10	wceq 1534	1 wff ℤ≥ = (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})

This definition is referenced by:  uzval  12854  uzf  12855