reserve x,y,y1,y2 for object;

theorem
  for GF be add-associative right_zeroed right_complementable Abelian
  associative well-unital distributive non empty doubleLoopStr, V be Abelian
  add-associative right_zeroed right_complementable vector-distributive
  scalar-distributive scalar-associative scalar-unital non empty
  ModuleStr over GF, V1 be Subset of V st the carrier of V = V1 holds V1 is
  linearly-closed;
