
theorem ThSL1:
  for L being Z_Lattice, L1 being Z_Sublattice of L holds
  L1 is Submodule of L
  proof
    let L be Z_Lattice, L1 be Z_Sublattice of L;
    A1: the carrier of L1 c= the carrier of L by defSublattice;
    A2: the addF of L1 = (the addF of L) || the carrier of L1 by defSublattice;
    A3: 0.L1 = 0.L by defSublattice;
    the lmult of L1 = (the lmult of L) |
    [:the carrier of INT.Ring, the carrier of L1:] by defSublattice;
    hence thesis by A1,A2,A3,VECTSP_4:def 2;
  end;
