 reserve n for Nat;

theorem
   for R being Ring, S being R-homomorphic Ring
   for h being Homomorphism of R,S holds
   h.(Product <*>(the carrier of R)) = 1.S
   proof
     let R be Ring, S be R-homomorphic Ring; let h be Homomorphism of R,S;
     thus h.(Product <*>(the carrier of R)) = h.(1_R) by GROUP_4:8
     .= 1_S by GROUP_1:def 13 .= 1.S;
   end;
