 reserve R for domRing;
 reserve p for odd prime Nat, m for positive Nat;
 reserve g for non zero Polynomial of INT.Ring;
 reserve f for Element of the carrier of Polynom-Ring INT.Ring;

theorem Th22:
  for p be odd prime Nat, m be positive Nat,k be Nat st 0 <= k <= p-'2 holds
  eval(~(((Der1(INT.Ring))|^k).f_0(m,p)),0.INT.Ring) = 0.INT.Ring
    proof
      let p be odd prime Nat, m be positive Nat, k be Nat;
      assume
A1:   0 <= k <= p-'2;
      set Fk = (((Der1(INT.Ring))|^k).f_0(m,p));
      eval(~Fk,0.INT.Ring) = (~Fk).0 by POLYNOM5:31;
      hence thesis by Th21,A1;
    end;
