
theorem Th2:
for V being RealLinearSpace,
    A,B being Subset of V
    st A c= the carrier of Lin B holds
    Lin A is Subspace of Lin B
proof
  let V be RealLinearSpace,
      A,B be Subset of V;
  assume A1: A c= the carrier of Lin B;
  reconsider D = the carrier of Lin B as Subset of V by RLSUB_1:def 2;
    Lin A is Subspace of Lin D by RLVECT_3:20,A1;
  hence thesis by RLVECT_3:18;
end;
