Definition df-uz 9621

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 9622 for its value, uzssz 9640 for its relationship to ℤ, nnuz 9656 and nn0uz 9655 for its relationships to ℕ and ℕ₀, and eluz1 9624 and eluz2 9626 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 9620	. 2 class ℤ≥
2		vj	. . 3 setvar 𝑗
3		cz 9345	. . 3 class ℤ
4	2	cv 1363	. . . . 5 class 𝑗
5		vk	. . . . . 6 setvar 𝑘
6	5	cv 1363	. . . . 5 class 𝑘
7		cle 8081	. . . . 5 class ≤
8	4, 6, 7	wbr 4034	. . . 4 wff 𝑗 ≤ 𝑘
9	8, 5, 3	crab 2479	. . 3 class {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘}
10	2, 3, 9	cmpt 4095	. 2 class (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})
11	1, 10	wceq 1364	1 wff ℤ≥ = (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})

This definition is referenced by:  uzval  9622  uzf  9623  uzennn  10547