Definition df-uz 9875

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 9876 for its value, uzssz 9895 for its relationship to ℤ, nnuz 9911 and nn0uz 9910 for its relationships to ℕ and ℕ₀, and eluz1 9878 and eluz2 9880 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 9874	. 2 class ℤ≥
2		vj	. . 3 setvar 𝑗
3		cz 9597	. . 3 class ℤ
4	2	cv 1397	. . . . 5 class 𝑗
5		vk	. . . . . 6 setvar 𝑘
6	5	cv 1397	. . . . 5 class 𝑘
7		cle 8325	. . . . 5 class ≤
8	4, 6, 7	wbr 4114	. . . 4 wff 𝑗 ≤ 𝑘
9	8, 5, 3	crab 2526	. . 3 class {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘}
10	2, 3, 9	cmpt 4176	. 2 class (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})
11	1, 10	wceq 1398	1 wff ℤ≥ = (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})

This definition is referenced by:  uzval  9876  uzf  9877  uzennn  10825