lean_workbook_plus_44546

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

Prove that if $ab \equiv ac \pmod{ad}$ , then $b \equiv c \pmod{d}$ and vice versa.

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_44546 (a b c d : ℤ) (ha : a ≠ 0) (hd : d ≠ 0) : (a * b ≡ a * c [ZMOD a * d]) ↔ (b ≡ c [ZMOD d])   :=  by sorry

Source