
theorem LCL1:
  for V be RealLinearSpace, V1 be Subset of V
  st V1 <> {} & V1 is linearly-closed
  holds the carrier of Lin(V1) = V1
  proof
    let V be RealLinearSpace, V1 be Subset of V;
    assume V1 <> {} & V1 is linearly-closed; then
    ex W0 being strict Subspace of V st V1 = the carrier of W0 by RLSUB_1:35;
    hence the carrier of Lin(V1) = V1 by RLVECT_3:18;
  end;
