
theorem ThSc3:
  for L being Z_Lattice, v, u being Vector of L, a being Element of INT.Ring
  holds <; v, a*u ;> = a * <; v, u ;>
  proof
    let L be Z_Lattice, v, u be Vector of L, a be Element of INT.Ring;
    thus <; v, a*u ;> = <; a*u, v ;> by defZLattice
    .= a * <; u, v ;> by defZLattice
    .= a * <; v, u ;> by defZLattice;
  end;
