Definition df-uz 9528

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 9529 for its value, uzssz 9546 for its relationship to ℤ, nnuz 9562 and nn0uz 9561 for its relationships to ℕ and ℕ₀, and eluz1 9531 and eluz2 9533 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 9527	. 2 class ℤ≥
2		vj	. . 3 setvar 𝑗
3		cz 9252	. . 3 class ℤ
4	2	cv 1352	. . . . 5 class 𝑗
5		vk	. . . . . 6 setvar 𝑘
6	5	cv 1352	. . . . 5 class 𝑘
7		cle 7992	. . . . 5 class ≤
8	4, 6, 7	wbr 4003	. . . 4 wff 𝑗 ≤ 𝑘
9	8, 5, 3	crab 2459	. . 3 class {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘}
10	2, 3, 9	cmpt 4064	. 2 class (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})
11	1, 10	wceq 1353	1 wff ℤ≥ = (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})

This definition is referenced by:  uzval  9529  uzf  9530  uzennn  10435