Definition df-uz 9932

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 9933 for its value, uzssz 9952 for its relationship to ℤ, nnuz 9968 and nn0uz 9967 for its relationships to ℕ and ℕ₀, and eluz1 9935 and eluz2 9937 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 9931	. 2 class ℤ≥
2		vj	. . 3 setvar 𝑗
3		cz 9649	. . 3 class ℤ
4	2	cv 1401	. . . . 5 class 𝑗
5		vk	. . . . . 6 setvar 𝑘
6	5	cv 1401	. . . . 5 class 𝑘
7		cle 8362	. . . . 5 class ≤
8	4, 6, 7	wbr 4130	. . . 4 wff 𝑗 ≤ 𝑘
9	8, 5, 3	crab 2532	. . 3 class {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘}
10	2, 3, 9	cmpt 4192	. 2 class (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})
11	1, 10	wceq 1402	1 wff ℤ≥ = (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})

This definition is used by:  uzval  9933  uzf  9934  uzennn  10887