Definition df-uz 9905

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 9906 for its value, uzssz 9925 for its relationship to ℤ, nnuz 9941 and nn0uz 9940 for its relationships to ℕ and ℕ₀, and eluz1 9908 and eluz2 9910 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 9904	. 2 class ℤ≥
2		vj	. . 3 setvar 𝑗
3		cz 9627	. . 3 class ℤ
4	2	cv 1401	. . . . 5 class 𝑗
5		vk	. . . . . 6 setvar 𝑘
6	5	cv 1401	. . . . 5 class 𝑘
7		cle 8355	. . . . 5 class ≤
8	4, 6, 7	wbr 4128	. . . 4 wff 𝑗 ≤ 𝑘
9	8, 5, 3	crab 2532	. . 3 class {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘}
10	2, 3, 9	cmpt 4190	. 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 referenced by:  uzval  9906  uzf  9907  uzennn  10856