Definition df-uz 12786

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 12787 for its value, uzssz 12806 for its relationship to ℤ, nnuz 12824 and nn0uz 12823 for its relationships to ℕ and ℕ₀, and eluz1 12789 and eluz2 12791 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 12785	. 2 class ℤ≥
2		vj	. . 3 setvar 𝑗
3		cz 12521	. . 3 class ℤ
4	2	cv 1541	. . . . 5 class 𝑗
5		vk	. . . . . 6 setvar 𝑘
6	5	cv 1541	. . . . 5 class 𝑘
7		cle 11177	. . . . 5 class ≤
8	4, 6, 7	wbr 5086	. . . 4 wff 𝑗 ≤ 𝑘
9	8, 5, 3	crab 3390	. . 3 class {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘}
10	2, 3, 9	cmpt 5167	. 2 class (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})
11	1, 10	wceq 1542	1 wff ℤ≥ = (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})

This definition is referenced by:  uzval  12787  uzf  12788