reserve d,i,j,k,m,n,p,q,x,k1,k2 for Nat,
  a,c,i1,i2,i3,i5 for Integer;

theorem Th52:
  Fermat(2) = 17
proof
  thus Fermat(2) = 2 |^ (2 |^ (1 + 1)) + 1
    .= 2 |^ (2 |^ 1 * 2) + 1 by NEWTON:6
    .= 2 |^ (3 + 1) + 1
    .= 2 |^ (2 + 1) * 2 + 1 by NEWTON:6
    .= 2 |^ (1 + 1) * 2 * 2 + 1 by NEWTON:6
    .= 2 |^ 1 * 2 * 2 * 2 + 1 by NEWTON:6
    .= 17;
end;
