
theorem NP1:
  for n be Nat holds (2*(n + 1)) choose (n + 1) = 2*((2*n + 1) choose n)
  proof
    let n be Nat;
    ((2*n + 1) + 1) choose (n + 1) =
      ((n + n + 1) choose n) + ((n + n + 1) choose (n+1)) by NEWTON:22
    .= (((n + 1) + n) choose n) + (((n + 1) + n) choose n) by N20
    .= 2* ((2*n + 1) choose n);
    hence thesis;
  end;
