theorem Th29:
  p `^ (n+1) = (p `^ n) *' p
proof
  set PR=Polynom-Ring (O, R);
  reconsider P=p as Element of PR by POLYNOM1:def 11;
  thus p `^ (n+1) = (power PR) . (P,n) * P by GROUP_1:def 7
  .= (p `^ n) *' p by POLYNOM1:def 11;
end;
