obtain ⟨c₁, rfl⟩ := (Coprime.dvd_mul_left h').mp <| Dvd.intro d h
a b c d : ℕ
h : a * d = b * c
h' : Coprime a b
⊢ ∃ m, c = m * a ∧ d = m * b
case intro
a b d : ℕ
h' : Coprime a b
c₁ : ℕ
h : a * d = b * (a * c₁)
⊢ ∃ m, a * c₁ = m * a ∧ d = m * b