
theorem for n be Nat holds
  (n choose 0) + ((n+2) choose 1) + ((n+4) choose 2) =
    ((n+5) choose 2) - (n+5) choose 0
  proof
    let n be Nat;
    (n choose 0) = 1 & (n + 1 + 1) choose 1 = n + 2 &
      ((n + 3) + 1) choose 2 = (n + 3)*(n + 4)/2 &
        ((n + 4) + 1) choose 2 = (n + 4)*(n + 5)/2 & (n + 5) choose 0 = 1
          by NEWTON:19,NUMPOLY1:72;
    hence thesis;
  end;
