
theorem Th20:
  for n being Nat st n > 0 holds Catalan n > 0
proof
  defpred P[Nat] means Catalan $1 > 0;
  let n be Nat;
  assume
A1: n > 0;
A2: for n being non zero Nat st P[n] holds P[n+1] by Th16;
A3: P[1] by Th11;
  for n being non zero Nat holds P[n] from NAT_1:sch 10(A3,A2);
  hence thesis by A1;
end;
