
theorem Th9:
  for a,b,c,d,n being Integer holds
  (a+b+c+d) mod n = ((a mod n)+(b mod n)+(c mod n)+(d mod n)) mod n
  proof
    let a,b,c,d,n be Integer;
    thus (a+b+c+d) mod n = ((a+b+c) mod n + (d mod n)) mod n by NAT_D:66
    .= ((((a mod n)+(b mod n)+(c mod n)) mod n) +((d mod n) mod n)) mod n
    by Th8
    .= ((a mod n)+(b mod n)+(c mod n)+(d mod n)) mod n by NAT_D:66;
  end;
