
theorem
  for L being Z_Lattice, L1 being Z_Sublattice of L,
  v1, v2 being Vector of L holds
  v1 in L1 & v2 in L1 implies v1 + v2 in L1
  proof
    let L be Z_Lattice, L1 be Z_Sublattice of L,
    v1, v2 be Vector of L;
    assume AS: v1 in L1 & v2 in L1;
    L1 is Submodule of L by ThSL1;
    hence thesis by AS,ZMODUL01:36;
  end;
