
theorem
  for p be Prime, n be Nat holds
  (n choose (p - 1)) mod p = ((n mod p) choose (p - 1)) mod p
  proof
    let p be Prime, n be Nat;
    (p - 1) + 0 < (p - 1) + 1 by XREAL_1:6;
    hence thesis by MOC;
  end;
