reserve i,j,k,n,m for Nat,
        X for set,
        b,s for bag of X,
        x for object;
reserve O for Ordinal,
        R for right_zeroed add-associative right_complementable
          right_unital distributive non trivial doubleLoopStr,
        p for Polynomial of O, R;

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;
