 reserve i,j, k,v, w for Nat;
 reserve j1,j2, m, n, s, t, x, y for Integer;
 reserve p for odd Prime;
 reserve a for Real;
 reserve b for Integer;

theorem Them5:
  for p be Prime holds
    ex x1,x2,x3,x4 be Nat st p = x1^2 + x2^2 + x3^2 + x4^2
  proof
    let p be Prime;
    per cases;
    suppose p is even;
      hence thesis by Them4;
    end;
    suppose p is odd;
      hence thesis by Them3;
    end;
  end;
