=> a phi psi; rewrite scalerAr -mulrDr; congr (_ * _).
rewrite linear_sum -big_split; apply: eq_bigr => x _ /=.by rewrite !cfunE mulrDl -mulrA.

(* Specifications: *)
Canonical cfdotr_additive xi :=
Proof. by rewrite -cfdotrE linear0. Qed.
Proof. by rewrite -!cfdotrE linearN. Qed.
phi \in 'CF(G, A) -> {in A, psi1 =1 psi2} -> '[phi, psi1] = '[phi, p