
theorem
  for p be Prime, k be non zero Nat st not p divides k holds
    (p choose (k mod p)) mod p = 0
  proof
    let p be Prime, k be non zero Nat such that
    A1: not p divides k;
    k mod p <> 0 by A1,PEPIN:6; then
    p > (k mod p) > 0 by NAT_D:1;
    hence thesis by PCK;
  end;
