
theorem
  for L being Z_Lattice, L1 being Z_Sublattice of L,
  v being Vector of L holds
  v in L1 implies -v in L1
  proof
    let L be Z_Lattice, L1 be Z_Sublattice of L, v be Vector of L;
    assume AS: v in L1;
    L1 is Submodule of L by ThSL1;
    hence thesis by AS,ZMODUL01:38;
  end;
