Definition df-uz 9177

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 9178 for its value, uzssz 9195 for its relationship to ℤ, nnuz 9211 and nn0uz 9210 for its relationships to ℕ and ℕ₀, and eluz1 9180 and eluz2 9182 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 9176	. 2 class ℤ≥
2		vj	. . 3 setvar 𝑗
3		cz 8906	. . 3 class ℤ
4	2	cv 1298	. . . . 5 class 𝑗
5		vk	. . . . . 6 setvar 𝑘
6	5	cv 1298	. . . . 5 class 𝑘
7		cle 7673	. . . . 5 class ≤
8	4, 6, 7	wbr 3875	. . . 4 wff 𝑗 ≤ 𝑘
9	8, 5, 3	crab 2379	. . 3 class {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘}
10	2, 3, 9	cmpt 3929	. 2 class (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})
11	1, 10	wceq 1299	1 wff ℤ≥ = (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})

This definition is referenced by:  uzval  9178  uzf  9179  uzennn  10050