reserve m, n for Nat;

theorem Th20:
  for n being Nat st ex p being non zero Nat
  st p <> 1 & p |^ 2 divides n holds n is square-containing
proof
  let n be Nat;
  given p being non zero Nat such that
A1: p <> 1 and
A2: p |^ 2 divides n;
  consider r being Prime such that
A3: r divides p by A1,Lm2;
  r |^ 2 divides p |^ 2 by A3,WSIERP_1:14;
  then r |^ 2 divides n by A2,NAT_D:4;
  hence thesis;
end;
