let L be Z_Lattice; :: thesis: for L1 being Z_Sublattice of L holds 0. L in L1
let L1 be Z_Sublattice of L; :: thesis: 0. L in L1
L1 is Submodule of L by ThSL1;
hence 0. L in L1 by ZMODUL01:33; :: thesis: verum