Definition df-uz 12990

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 12991 for its value, uzssz 13010 for its relationship to ℤ, nnuz 13028 and nn0uz 13027 for its relationships to ℕ and ℕ₀, and eluz1 12993 and eluz2 12995 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 12989	. 2 class ℤ≥
2		vj	. . 3 setvar 𝑗
3		cz 12717	. . 3 class ℤ
4	2	cv 1569	. . . . 5 class 𝑗
5		vk	. . . . . 6 setvar 𝑘
6	5	cv 1569	. . . . 5 class 𝑘
7		cle 11368	. . . . 5 class ≤
8	4, 6, 7	wbr 5106	. . . 4 wff 𝑗 ≤ 𝑘
9	8, 5, 3	crab 3416	. . 3 class {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘}
10	2, 3, 9	cmpt 5189	. 2 class (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})
11	1, 10	wceq 1570	1 wff ℤ≥ = (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})

This definition is used by:  uzval  12991  uzf  12992