Definition df-uz 11880

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 11881 for its value, uzssz 11899 for its relationship to ℤ, nnuz 11916 and nn0uz 11915 for its relationships to ℕ and ℕ₀, and eluz1 11883 and eluz2 11885 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 11879	. 2 class ℤ≥
2		vj	. . 3 setvar 𝑗
3		cz 11569	. . 3 class ℤ
4	2	cv 1631	. . . . 5 class 𝑗
5		vk	. . . . . 6 setvar 𝑘
6	5	cv 1631	. . . . 5 class 𝑘
7		cle 10267	. . . . 5 class ≤
8	4, 6, 7	wbr 4804	. . . 4 wff 𝑗 ≤ 𝑘
9	8, 5, 3	crab 3054	. . 3 class {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘}
10	2, 3, 9	cmpt 4881	. 2 class (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})
11	1, 10	wceq 1632	1 wff ℤ≥ = (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})

This definition is referenced by:  uzval  11881  uzf  11882