
theorem Th13:
  for n being Nat holds Catalan (n) is Integer
proof
  let n be Nat;
  per cases by NAT_1:25;
  suppose
    n = 0;
    hence thesis;
  end;
  suppose
    n = 1;
    hence thesis;
  end;
  suppose
    n > 1;
    then Catalan n = 4 * ((2*n -' 3) choose (n -' 1)) - ((2*n -' 1) choose (n
    -' 1)) by Th9;
    hence thesis;
  end;
end;
