Definition df-uz 9619

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 9620 for its value, uzssz 9638 for its relationship to ℤ, nnuz 9654 and nn0uz 9653 for its relationships to ℕ and ℕ₀, and eluz1 9622 and eluz2 9624 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 9618	. 2 class ℤ≥
2		vj	. . 3 setvar 𝑗
3		cz 9343	. . 3 class ℤ
4	2	cv 1363	. . . . 5 class 𝑗
5		vk	. . . . . 6 setvar 𝑘
6	5	cv 1363	. . . . 5 class 𝑘
7		cle 8079	. . . . 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  9620  uzf  9621  uzennn  10545