import data.int data.real
open algebra nat int rat real

example : (1 : ℤ) * (1 : ℤ) = (1 : ℤ) :=
sorry

example : (1 : ℤ) * 1 = 1 :=
sorry

example : (1 : ℝ) * (1 : ℝ) = (1 : ℝ) :=
sorry

example : (1 : ℝ) * 1 = 1 :=
sorry

variable x : ℝ
variable a : ℤ
variable n : ℕ

example : x + a + n + 1 = 1 :=
sorry

example : x + 1 = 1 + x :=
sorry