theorem
  K is having_valuation & a is Element of ValuatRing v implies
  power(K).(a,n) is Element of ValuatRing v
  proof
    assume
A1: K is having_valuation;
    assume a is Element of ValuatRing v;
    then reconsider y = a as Element of ValuatRing v;
    reconsider n as Element of NAT by ORDINAL1:def 12;
    power(ValuatRing v).(y,n) is Element of ValuatRing v;
    hence thesis by A1,Th60;
  end;
