Prove2Me

`BookProof.ChapterPinOmega.Omega_mul_closed` : ∀ x ∈ Omega, ∀ y ∈ Omega, x * y ∈ Omega

Proved
BookProof.ChapterPinOmega.Omega_mul_closed

by leonardopedro · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterPinOmega.

BookProof.ChapterPinOmega.Omega_mul_closed : ∀ x ∈ Omega, ∀ y ∈ Omega, x * y ∈ Omega

Formalization note: Lean 4 identifier BookProof.ChapterPinOmega.Omega_mul_closed.

Preamble
-- Generated from ChapterPinOmega.lean — theorem BookProof.ChapterPinOmega.Omega_mul_closed
import Definitions.Def_ChapterA3
import Mathlib
import Definitions.Def_ChapterPinOmega
import Definitions.Def_ChapterPinDoubleCover
open BookProof.ChapterPinDoubleCover
open BookProof.ChapterPinOmega


open Matrix


open BookProof.ChapterA3
Formal statement
theorem BookProof.ChapterPinOmega.Omega_mul_closed : ∀ x ∈ Omega, ∀ y ∈ Omega, x * y ∈ Omega := by sorry

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