
theorem ThSc2:
  for L being Z_Lattice, v, u, w being Vector of L holds
  <; v, u + w ;> = <; v, u ;> + <; v, w ;>
  proof
    let L be Z_Lattice, v, u, w be Vector of L;
    thus <; v, u+w ;> = <; u+w, v ;> by defZLattice
    .= <; u, v ;> + <; w, v ;> by defZLattice
    .= <; v, u ;> + <; w, v ;> by defZLattice
    .= <; v, u ;> + <; v, w ;> by defZLattice;
  end;
