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

Proved

BookProof.ChapterFiniteArithmeticPrior.truncMul_eq_mul

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterFiniteArithmeticPrior.

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

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

Preamble

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

Formal statement

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

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