End RingTheory.
Section RightRegular.
Variable R : ringType.
Implicit Types x y : R.
Let Rc := converse_ringType R.

(* Specifications: *)
Lemma mulIr_eq0 x y : rreg x -> (y * x == 0) = (y == 0).
Lemma scaler_sign (b : bool) v: (-1) ^+ b *: v = (if b then - v else v).
Lemma scalerMnr a v n : a *: v *+ n = a *: (v *+ n).
Lemma scaler_suml v I r (P : pred I) F :
(\sum_(i <- r | P i) F i) *: v = \sum_(i <- r | P i) F i *: v.