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

theorem Th18:
   for n be Ordinal,L
   for a,b being Element of L, p being Series of n,L holds (a*b)*p = a*(b*p)
   proof
     let n be Ordinal, L;
     let a,b be Element of L, p be Series of n,L;
     for i be Element of Bags n holds ((a*b)*p).i = (a*(b*p)).i
     proof
       let i be Element of Bags n;
       thus ((a*b)*p).i = (a*b)*p.i by POLYNOM7:def 9
       .= a*(b*(p.i)) by GROUP_1:def 3 .= a*(b*p).i by POLYNOM7:def 9
       .= (a*(b*p)).i by POLYNOM7:def 9;
     end;
     hence thesis;
   end;
