Definition df-uz 12059

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 12060 for its value, uzssz 12078 for its relationship to ℤ, nnuz 12095 and nn0uz 12094 for its relationships to ℕ and ℕ₀, and eluz1 12062 and eluz2 12064 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 12058	. 2 class ℤ≥
2		vj	. . 3 setvar 𝑗
3		cz 11793	. . 3 class ℤ
4	2	cv 1506	. . . . 5 class 𝑗
5		vk	. . . . . 6 setvar 𝑘
6	5	cv 1506	. . . . 5 class 𝑘
7		cle 10475	. . . . 5 class ≤
8	4, 6, 7	wbr 4929	. . . 4 wff 𝑗 ≤ 𝑘
9	8, 5, 3	crab 3092	. . 3 class {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘}
10	2, 3, 9	cmpt 5008	. 2 class (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})
11	1, 10	wceq 1507	1 wff ℤ≥ = (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})

This definition is referenced by:  uzval  12060  uzf  12061