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