Definition df-uz 9853

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 9854 for its value, uzssz 9873 for its relationship to ℤ, nnuz 9889 and nn0uz 9888 for its relationships to ℕ and ℕ₀, and eluz1 9856 and eluz2 9858 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 9852	. 2 class ℤ≥
2		vj	. . 3 setvar 𝑗
3		cz 9576	. . 3 class ℤ
4	2	cv 1397	. . . . 5 class 𝑗
5		vk	. . . . . 6 setvar 𝑘
6	5	cv 1397	. . . . 5 class 𝑘
7		cle 8308	. . . . 5 class ≤
8	4, 6, 7	wbr 4108	. . . 4 wff 𝑗 ≤ 𝑘
9	8, 5, 3	crab 2524	. . 3 class {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘}
10	2, 3, 9	cmpt 4170	. 2 class (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})
11	1, 10	wceq 1398	1 wff ℤ≥ = (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})

This definition is referenced by:  uzval  9854  uzf  9855  uzennn  10797