
theorem for n be Nat holds
  (n choose 0) + ((n+2) choose 1) +
    ((n + 4) choose 2) + ((n + 6) choose 3) =
      ((n + 7) choose 3) - ((n + 6) choose 1)
  proof
    let n be Nat;
    (n choose 0) = 1 & (n+1+1) choose 1 = n+2 &
      (n + 4) choose 2 = (n + 4)*((n+4)-1)/2 &
        (n + 6) choose 3 = (n+6)*((n+6)-1)*((n+6)-2)/6 &
          (n + 7) choose 3 = (n + 7)*((n + 7)-1)*((n+7)-2)/6 &
            (n + 6) choose 1 = n + 6 by STIRL2_1:51,NEWTON:19;
    hence thesis;
  end;
