let GF be non empty right_complementable well-unital distributive Abelian add-associative right_zeroed associative doubleLoopStr ; :: thesis: for M being non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed ModuleStr over GF holds LattStr(# (Subspaces M),(SubJoin M),(SubMeet M) #) is 01_Lattice
let M be non empty right_complementable vector-distributive scalar-distributive scalar-associative scalar-unital Abelian add-associative right_zeroed ModuleStr over GF; :: thesis: LattStr(# (Subspaces M),(SubJoin M),(SubMeet M) #) is 01_Lattice
LattStr(# (Subspaces M),(SubJoin M),(SubMeet M) #) is lower-bounded upper-bounded Lattice by Th58, Th59;
hence LattStr(# (Subspaces M),(SubJoin M),(SubMeet M) #) is 01_Lattice ; :: thesis: verum