Definition df-uz 9529

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 9530 for its value, uzssz 9547 for its relationship to ℤ, nnuz 9563 and nn0uz 9562 for its relationships to ℕ and ℕ₀, and eluz1 9532 and eluz2 9534 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 9528	. 2 class ℤ≥
2		vj	. . 3 setvar 𝑗
3		cz 9253	. . 3 class ℤ
4	2	cv 1352	. . . . 5 class 𝑗
5		vk	. . . . . 6 setvar 𝑘
6	5	cv 1352	. . . . 5 class 𝑘
7		cle 7993	. . . . 5 class ≤
8	4, 6, 7	wbr 4004	. . . 4 wff 𝑗 ≤ 𝑘
9	8, 5, 3	crab 2459	. . 3 class {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘}
10	2, 3, 9	cmpt 4065	. 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  9530  uzf  9531  uzennn  10436