Section FrobeniusAutomorphism.
Variables (p : nat) (charRp : p \in [char R]).
Canonical Frobenius_aut_additive := Additive Frobenius_aut_is_rmorphism.
Canonical Frobenius_aut_rmorphism := RMorphism Frobenius_aut_is_rmorphism.
End FrobeniusAutomorphism.

Lemma scaler_prod I r (P : pred I) (F : I -> R) (G : I -> A) :
\prod_(i <- r | P i) (F i *: G i) =
\prod_(i <- r | P i) F i *: \prod_(i <- r | P i) G i.