Definition df-uz 12754

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 12755 for its value, uzssz 12774 for its relationship to ℤ, nnuz 12796 and nn0uz 12795 for its relationships to ℕ and ℕ₀, and eluz1 12757 and eluz2 12759 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 12753	. 2 class ℤ≥
2		vj	. . 3 setvar 𝑗
3		cz 12489	. . 3 class ℤ
4	2	cv 1539	. . . . 5 class 𝑗
5		vk	. . . . . 6 setvar 𝑘
6	5	cv 1539	. . . . 5 class 𝑘
7		cle 11169	. . . . 5 class ≤
8	4, 6, 7	wbr 5095	. . . 4 wff 𝑗 ≤ 𝑘
9	8, 5, 3	crab 3396	. . 3 class {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘}
10	2, 3, 9	cmpt 5176	. 2 class (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})
11	1, 10	wceq 1540	1 wff ℤ≥ = (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})

This definition is referenced by:  uzval  12755  uzf  12756