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

theorem Th47:
   for p,q be Element of Polynom-Ring(1,R),
   f,g be Element of Formal-Series(1,R) st p = f & q = g holds p*q = f * g
   proof
     let p,q be Element of Polynom-Ring(1,R),
     f,g be Element of Formal-Series(1,R);
     assume
A1:  p = f & q = g;
     reconsider p0 = p,q0 =q as Polynomial of 1,R by POLYNOM1:def 11;
     reconsider p1 = p0, q1 = q0 as Series of 1,R;
     p*q = p0 *' q0 by POLYNOM1:def 11 .= f * g by A1,Def3;
     hence thesis;
   end;
