Definition df-uz 12847

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 12848 for its value, uzssz 12867 for its relationship to ℤ, nnuz 12889 and nn0uz 12888 for its relationships to ℕ and ℕ₀, and eluz1 12850 and eluz2 12852 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 12846	. 2 class ℤ≥
2		vj	. . 3 setvar 𝑗
3		cz 12582	. . 3 class ℤ
4	2	cv 1533	. . . . 5 class 𝑗
5		vk	. . . . . 6 setvar 𝑘
6	5	cv 1533	. . . . 5 class 𝑘
7		cle 11273	. . . . 5 class ≤
8	4, 6, 7	wbr 5142	. . . 4 wff 𝑗 ≤ 𝑘
9	8, 5, 3	crab 3428	. . 3 class {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘}
10	2, 3, 9	cmpt 5225	. 2 class (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})
11	1, 10	wceq 1534	1 wff ℤ≥ = (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})

This definition is referenced by:  uzval  12848  uzf  12849