reserve FS for non empty doubleLoopStr;
reserve F for Field;
reserve R for Abelian add-associative right_zeroed right_complementable non
  empty addLoopStr,
  x, y, z for Scalar of R;
reserve SF for Skew-Field,
  x, y, z for Scalar of SF;

theorem
  z<>0.SF implies x/z + y/z = (x+y)/z & x/z - y/z = (x-y)/z
proof
  z<>0.SF implies x/z - y/z = (x-y)/z
  proof
    assume z<>0.SF;
    hence x/z - y/z =x/z+(-y)/z by Th19
      .=(x-y)/z by VECTSP_1:def 7;
  end;
  hence thesis by VECTSP_1:def 7;
end;
