Definition df-uz 12966

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 12967 for its value, uzssz 12986 for its relationship to ℤ, nnuz 13004 and nn0uz 13003 for its relationships to ℕ and ℕ₀, and eluz1 12969 and eluz2 12971 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 12965	. 2 class ℤ≥
2		vj	. . 3 setvar 𝑗
3		cz 12693	. . 3 class ℤ
4	2	cv 1568	. . . . 5 class 𝑗
5		vk	. . . . . 6 setvar 𝑘
6	5	cv 1568	. . . . 5 class 𝑘
7		cle 11344	. . . . 5 class ≤
8	4, 6, 7	wbr 5102	. . . 4 wff 𝑗 ≤ 𝑘
9	8, 5, 3	crab 3412	. . 3 class {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘}
10	2, 3, 9	cmpt 5185	. 2 class (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})
11	1, 10	wceq 1569	1 wff ℤ≥ = (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})

This definition is used by:  uzval  12967  uzf  12968