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

phi \in 'CF(G, A) -> {in A, psi1 =1 psi2} -> '[phi, psi1] = '[phi, p