`BookProof.ChapterFiniteArithmeticPrior.truncMul_saturates` {B : ℕ} [NeZero B] (a b : Fin B) (h : ¬ (a : ℕ) * (b : ℕ) < B) : (((truncMul B).result a b : Fin B) : ℕ) = B - 1

Proved

BookProof.ChapterFiniteArithmeticPrior.truncMul_saturates

by leonardopedro · Oct 8, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterFiniteArithmeticPrior.

BookProof.ChapterFiniteArithmeticPrior.truncMul_saturates {B : ℕ} [NeZero B] (a b : Fin B) (h : ¬ (a : ℕ) * (b : ℕ) < B) : (((truncMul B).result a b : Fin B) : ℕ) = B - 1

Formalization note: Lean 4 identifier BookProof.ChapterFiniteArithmeticPrior.truncMul_saturates.

Preamble

-- Generated from ChapterFiniteArithmeticPrior.lean — theorem BookProof.ChapterFiniteArithmeticPrior.truncMul_saturates
import Mathlib
import Definitions.Def_ChapterFiniteArithmeticPrior
open BookProof.ChapterFiniteArithmeticPrior

Formal statement

theorem BookProof.ChapterFiniteArithmeticPrior.truncMul_saturates {B : ℕ} [NeZero B] (a b : Fin B)
    (h : ¬ (a : ℕ) * (b : ℕ) < B) :
    (((truncMul B).result a b : Fin B) : ℕ) = B - 1 := by sorry

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