
theorem
  for n be even Nat holds Parity (n!) = Parity ((n+1)!)
  proof
    let n be even Nat;
    Parity (n + 1) = 1 by NAT_2:def 1; then
    Parity ((n + 1)!) = 1*(Parity (n!)) by PAS;
    hence thesis;
  end;
