attribute [local simp] Nat.mul_comm Nat.mul_assoc Nat.mul_left_comm
attribute [local simp] Nat.add_assoc Nat.add_comm Nat.add_left_comm
example (w x y z : Nat) (p : Nat → Prop)
        (h : p (x * y + z * w  * x)) : p (x * w * z + y * x) := by
  simp at *; assumption

example (x y z : Nat) (p : Nat → Prop)
        (h₁ : p (1 * x + y)) (h₂ : p  (x * z * 1))
        : p (y + 0 + x) ∧ p (z * x) := by
  simp at * <;> constructor <;> assumption