Definition df-uz 12891

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 12892 for its value, uzssz 12911 for its relationship to ℤ, nnuz 12929 and nn0uz 12928 for its relationships to ℕ and ℕ₀, and eluz1 12894 and eluz2 12896 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 12890	. 2 class ℤ≥
2		vj	. . 3 setvar 𝑗
3		cz 12618	. . 3 class ℤ
4	2	cv 1569	. . . . 5 class 𝑗
5		vk	. . . . . 6 setvar 𝑘
6	5	cv 1569	. . . . 5 class 𝑘
7		cle 11271	. . . . 5 class ≤
8	4, 6, 7	wbr 5107	. . . 4 wff 𝑗 ≤ 𝑘
9	8, 5, 3	crab 3414	. . 3 class {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘}
10	2, 3, 9	cmpt 5190	. 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  12892  uzf  12893