 reserve o,o1,o2 for object;
 reserve n for Ordinal;
 reserve R,L for non degenerated comRing;
 reserve b for bag of 1;

theorem Th29:
   for f,g be Element of Formal-Series(1,R) holds
   (BSFSeri(R)).(f*g) = (BSFSeri(R)).f * (BSFSeri(R)).g
   proof
     let f,g be Element of Formal-Series(1,R);
     consider f1 being Series of 1,R such that
A1:  f1 = f & (BSFSeri(R)).f = f1*(NBag1) by Def4;
     consider g1 being Series of 1,R such that
A2:  g1 = g & (BSFSeri(R)).g = g1*(NBag1) by Def4;
     consider fg1 being Series of 1,R such that
A3:  fg1 = f*g & (BSFSeri(R)).(f*g) = fg1*(NBag1) by Def4;
A4:  fg1 = f1 *' g1 by A1,A2,A3,Def3;
     (BSFSeri(R)).(f*g) = (f1*(NBag1)) *' (g1*(NBag1)) by A3,A4,Th28
     .= (BSFSeri(R)).f * (BSFSeri(R)).g by A1,A2,POLYALG1:def 2;
     hence thesis;
   end;
