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
  for p be prime Nat holds a divides p|^n implies ex k st a = p|^k
proof
  let p be prime Nat;
  assume a divides p|^n; then
  ex k be Nat st a = p|^k & k <= n by GROUPP_1:2;
  hence thesis;
end;
