Definition df-uz 9488

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 9489 for its value, uzssz 9506 for its relationship to ℤ, nnuz 9522 and nn0uz 9521 for its relationships to ℕ and ℕ₀, and eluz1 9491 and eluz2 9493 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 9487	. 2 class ℤ≥
2		vj	. . 3 setvar 𝑗
3		cz 9212	. . 3 class ℤ
4	2	cv 1347	. . . . 5 class 𝑗
5		vk	. . . . . 6 setvar 𝑘
6	5	cv 1347	. . . . 5 class 𝑘
7		cle 7955	. . . . 5 class ≤
8	4, 6, 7	wbr 3989	. . . 4 wff 𝑗 ≤ 𝑘
9	8, 5, 3	crab 2452	. . 3 class {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘}
10	2, 3, 9	cmpt 4050	. 2 class (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})
11	1, 10	wceq 1348	1 wff ℤ≥ = (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})

This definition is referenced by:  uzval  9489  uzf  9490  uzennn  10392