
theorem Th16:
  for n being Nat holds Catalan (n) <= Catalan (n + 1)
proof
  let n be Nat;
  per cases by NAT_1:25;
  suppose
    n = 0;
    hence thesis;
  end;
  suppose
    n = 1;
    hence thesis by Th11,Th12;
  end;
  suppose
    n > 1;
    hence thesis by Th15;
  end;
end;
