reserve m, n for Nat;

theorem Th10:
  for a being Nat, p being Prime holds p |^ 2 divides a implies p divides a
proof
  let a be Nat;
  let p be Prime;
  assume p |^ 2 divides a;
  then consider t being Nat such that
A1: a = (p |^ 2) * t by NAT_D:def 3;
  a = (p * p) * t by A1,WSIERP_1:1
    .= p * (p * t);
  hence thesis by NAT_D:def 3;
end;
