Definition df-uz 12876

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 12877 for its value, uzssz 12896 for its relationship to ℤ, nnuz 12918 and nn0uz 12917 for its relationships to ℕ and ℕ₀, and eluz1 12879 and eluz2 12881 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 12875	. 2 class ℤ≥
2		vj	. . 3 setvar 𝑗
3		cz 12610	. . 3 class ℤ
4	2	cv 1535	. . . . 5 class 𝑗
5		vk	. . . . . 6 setvar 𝑘
6	5	cv 1535	. . . . 5 class 𝑘
7		cle 11293	. . . . 5 class ≤
8	4, 6, 7	wbr 5147	. . . 4 wff 𝑗 ≤ 𝑘
9	8, 5, 3	crab 3432	. . 3 class {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘}
10	2, 3, 9	cmpt 5230	. 2 class (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})
11	1, 10	wceq 1536	1 wff ℤ≥ = (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})

This definition is referenced by:  uzval  12877  uzf  12878