 reserve n for Nat;

theorem
   for R being Ring, S being R-homomorphic Ring
   for h being Homomorphism of R,S
   for F,G being FinSequence of R holds h.(Sum(F^G)) = h.(Sum F) + h.(Sum G)
   proof
     let R be Ring, S be R-homomorphic Ring; let h be Homomorphism of R,S;
     let F,G be FinSequence of R;
     thus h.(Sum(F^G)) = h.(Sum F + Sum G) by RLVECT_1:41
     .= h.(Sum F) + h.(Sum G) by VECTSP_1:def 20;
  end;
