
theorem
  for L being Z_Lattice, L1 being Z_Sublattice of L,
  v1, v2 being Vector of L, w1, w2 being Vector of L1 holds
  w1 = v1 & w2 = v2 implies w1 + w2 = v1 + v2
  proof
    let L be Z_Lattice, L1 be Z_Sublattice of L,
    v1, v2 be Vector of L, w1, w2 be Vector of L1;
    assume AS: w1 = v1 & w2 = v2;
    L1 is Submodule of L by ThSL1;
    hence thesis by AS,ZMODUL01:28;
  end;
