Definition df-uz 12935

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 12936 for its value, uzssz 12955 for its relationship to ℤ, nnuz 12973 and nn0uz 12972 for its relationships to ℕ and ℕ₀, and eluz1 12938 and eluz2 12940 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 12934	. 2 class ℤ≥
2		vj	. . 3 setvar 𝑗
3		cz 12662	. . 3 class ℤ
4	2	cv 1569	. . . . 5 class 𝑗
5		vk	. . . . . 6 setvar 𝑘
6	5	cv 1569	. . . . 5 class 𝑘
7		cle 11315	. . . . 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 1570	1 wff ℤ≥ = (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})

This definition is used by:  uzval  12936  uzf  12937