
theorem
  for L being Z_Lattice, L1 being Z_Sublattice of L,
  v being Vector of L, w being Vector of L1, a being Element of INT.Ring holds
  w = v implies a * w = a * v
  proof
    let L be Z_Lattice, L1 be Z_Sublattice of L,
    v be Vector of L, w be Vector of L1, a be Element of INT.Ring;
    assume AS: w = v;
    L1 is Submodule of L by ThSL1;
    hence thesis by AS,ZMODUL01:29;
  end;
