Section RingTheory.
Variable R : ringType.
Implicit Types x y : R.

Lemma mulrA : @associative R *%R. Proof. by case R => T [? []]. Qed.
Lemma mul1r : @left_id R R 1 *%R. Proof. by case R => T [? []]. Qed.
Lemma mulr1 : @right_id R R 1 *%R. Proof. by case R => T [? []]. Qed.
Lemma mulrDl : @left_distributive R R *%R +%R.
Lemma mulr0 : @right_zero R R 0 *%R.
Lemma mulrN x y : x * (- y) = - (x * y).