
theorem Th17:
  for V being RealLinearSpace, M being non empty Affine Subset of
  V, u,v being VECTOR of V st u in M & v in M holds M - {v} = M - {u}
proof
  let V be RealLinearSpace;
  let M be non empty Affine Subset of V;
  let u,v be VECTOR of V;
  assume u in M & v in M;
  then (ex N1 being non empty Affine Subset of V st N1 = M - {u} & M
is_parallel_to N1 & N1 is Subspace-like )& ex N2 being non empty Affine Subset
  of V st N2 = M - {v} & M is_parallel_to N2 & N2 is Subspace-like by Th16;
  hence thesis by Th14;
end;
