reserve a,b,m,x,n,l,xi,xj for Nat,
  t,z for Integer;

theorem Th7:
  for l,m,n being Integer holds (l*m) mod n = (l*(m mod n)) mod n
proof
  let l,m,n be Integer;
  thus (l*(m mod n)) mod n = ((l mod n)*((m mod n)mod n)) mod n by NAT_D:67
  .= ((l mod n)*(m mod n)) mod n by NAT_D:73
  .= (l*m) mod n by NAT_D:67;
end;
