Definition df-uz 11673

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 11674 for its value, uzssz 11692 for its relationship to ℤ, nnuz 11708 and nn0uz 11707 for its relationships to ℕ and ℕ₀, and eluz1 11676 and eluz2 11678 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 11672	. 2 class ℤ≥
2		vj	. . 3 setvar 𝑗
3		cz 11362	. . 3 class ℤ
4	2	cv 1480	. . . . 5 class 𝑗
5		vk	. . . . . 6 setvar 𝑘
6	5	cv 1480	. . . . 5 class 𝑘
7		cle 10060	. . . . 5 class ≤
8	4, 6, 7	wbr 4644	. . . 4 wff 𝑗 ≤ 𝑘
9	8, 5, 3	crab 2913	. . 3 class {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘}
10	2, 3, 9	cmpt 4720	. 2 class (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})
11	1, 10	wceq 1481	1 wff ℤ≥ = (𝑗 ∈ ℤ ↦ {𝑘 ∈ ℤ ∣ 𝑗 ≤ 𝑘})

This definition is referenced by:  uzval  11674  uzf  11675