Definition df-uz 9937

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 9938 for its value, uzssz 9957 for its relationship to ℤ, nnuz 9973 and nn0uz 9972 for its relationships to ℕ and ℕ₀, and eluz1 9940 and eluz2 9942 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 9936	. 2 class ℤ≥
2		vj	. . 3 setvar 𝑗
3		cz 9653	. . 3 class ℤ
4	2	cv 1401	. . . . 5 class 𝑗
5		vk	. . . . . 6 setvar 𝑘
6	5	cv 1401	. . . . 5 class 𝑘
7		cle 8367	. . . . 5 class ≤
8	4, 6, 7	wbr 4131	. . . 4 wff 𝑗 ≤ 𝑘
9	8, 5, 3	crab 2532	. . 3 class {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘}
10	2, 3, 9	cmpt 4193	. 2 class (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})
11	1, 10	wceq 1402	1 wff ℤ≥ = (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})

This definition is used by:  uzval  9938  uzf  9939  uzennn  10893