 reserve n,s for Nat;

theorem Th35:
  for s being non trivial Nat,
      x being s-gonal number holds
    0 <= ((8 * s - 16) * x) + (s - 4) ^2
  proof
    let s be non trivial Nat;
    let x be s-gonal number;
    s - 2 >= 2 - 2 by XREAL_1:9,NAT_2:29; then
    8 * (s - 2) >= 0;
    hence thesis;
  end;
