
theorem
  for p1,p2 be Safe Prime, N be Nat st p1 <> p2 & N = p1*p2 holds
  ex q1,q2 be Sophie_Germain Prime st Euler (N) = 4*q1*q2
proof
  let p1,p2 be Safe Prime, N be Nat;
  assume that
A1: p1 <> p2 and
A2: N = p1*p2;
  consider q2 be Sophie_Germain Prime such that
A4: Euler p2 = 2*q2 by Th11;
  consider q1 be Sophie_Germain Prime such that
A5: Euler p1 = 2*q1 by Th11;
  Euler N = Euler p1 * Euler p2 by A1,A2,EULER_1:21,INT_2:30
    .= 4*q1*q2 by A5,A4;
  hence thesis;
end;
