reserve a,b,c,d,x,j,k,l,m,n,o,xi,xj for Nat,
  p,q,t,z,u,v for Integer,
  a1,b1,c1,d1 for Complex;

theorem NAT332:
  for a be prime Nat, b be non zero Integer, c be Nat holds
  a |-count (b|^c) = c*(a |-count b)
  proof
    let a be prime Nat, b be non zero Integer, c be Nat;
    a |-count (b|^c) = a |-count (|.b.||^c) by TAYLOR_2:1
    .= c*(a|-count |.b.|) by NAT_3:32;
    hence thesis;
  end;
