
theorem CPP:
  for a,b,c be Nat holds ((a + 1) choose (b + 1)) mod c =
  (((a choose b) mod c) + ((a choose (b + 1)) mod c)) mod c
  proof
    let a,b,c be Nat;
    ((a + 1) choose (b + 1)) mod c =
      ((a choose b) + (a choose (b + 1))) mod c by NEWTON:22
    .= (((a choose b) mod c) + ((a choose (b + 1)) mod c)) mod c by NAT_D:66;
  hence thesis;
end;
