no goals
α : Type u
inst✝² : Group α
inst✝¹ : LT α
inst✝ : CovariantClass α α (fun x x_1 => x * x_1) fun x x_1 => x < x_1
a b c : α
⊢ b⁻¹ * a < c ↔ a < b * c
rw [← mul_lt_mul_iff_left b, mul_inv_cancel_left]