Definition df-uz 9924

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 9925 for its value, uzssz 9944 for its relationship to ℤ, nnuz 9960 and nn0uz 9959 for its relationships to ℕ and ℕ₀, and eluz1 9927 and eluz2 9929 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 9923	. 2 class ℤ≥
2		vj	. . 3 setvar 𝑗
3		cz 9646	. . 3 class ℤ
4	2	cv 1401	. . . . 5 class 𝑗
5		vk	. . . . . 6 setvar 𝑘
6	5	cv 1401	. . . . 5 class 𝑘
7		cle 8361	. . . . 5 class ≤
8	4, 6, 7	wbr 4130	. . . 4 wff 𝑗 ≤ 𝑘
9	8, 5, 3	crab 2532	. . 3 class {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘}
10	2, 3, 9	cmpt 4192	. 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  9925  uzf  9926  uzennn  10875