 reserve n for Nat;

theorem
   for R being Ring, S being R-homomorphic Ring
   for h being Homomorphism of R,S
   for F being FinSequence of R, a being Element of R holds
   h.(Sum(<*a*>^F)) = h.a + h.(Sum F)
   proof
      let R be Ring, S be R-homomorphic Ring; let h be Homomorphism of R,S;
      let F be FinSequence of R, a be Element of R;
      thus h.(Sum(<*a*>^F)) = h.(Sum(<*a*>) + Sum F) by RLVECT_1:41
                     .= h.(Sum<*a*>) + h.(Sum F) by VECTSP_1:def 20
                     .= h.a + h.(Sum F) by RLVECT_1:44;
   end;
