 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.(Product(<*a*>^F)) = h.a * h.(Product 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.(Product(<*a*>^F)) = h.(Product(<*a*>) * Product F) by GROUP_4:5
                         .= h.(Product<*a*>) * h.(Product F) by GROUP_6:def 6
                         .= h.a * h.(Product F) by GROUP_4:9;
   end;
