rw [← mul_assoc, ← mul_assoc, mul_comm b] at h
case intro.intro.inr
a b : ℕ
h' : Coprime a b
c₁ d₁ : ℕ
h : a * (b * d₁) = b * (a * c₁)
H : a * b ≠ 0
⊢ ∃ m, a * c₁ = m * a ∧ b * d₁ = m * b
case intro.intro.inr
a b : ℕ
h' : Coprime a b
c₁ d₁ : ℕ
h : a * b * d₁ = a * b * c₁
H : a * b ≠ 0
⊢ ∃ m, a * c₁ = m * a ∧ b * d₁ = m * b