Definition df-uz 12766

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 12767 for its value, uzssz 12786 for its relationship to ℤ, nnuz 12804 and nn0uz 12803 for its relationships to ℕ and ℕ₀, and eluz1 12769 and eluz2 12771 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 12765	. 2 class ℤ≥
2		vj	. . 3 setvar 𝑗
3		cz 12502	. . 3 class ℤ
4	2	cv 1541	. . . . 5 class 𝑗
5		vk	. . . . . 6 setvar 𝑘
6	5	cv 1541	. . . . 5 class 𝑘
7		cle 11181	. . . . 5 class ≤
8	4, 6, 7	wbr 5100	. . . 4 wff 𝑗 ≤ 𝑘
9	8, 5, 3	crab 3401	. . 3 class {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘}
10	2, 3, 9	cmpt 5181	. 2 class (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})
11	1, 10	wceq 1542	1 wff ℤ≥ = (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})

This definition is referenced by:  uzval  12767  uzf  12768