reserve V for RealLinearSpace;

theorem Th8:
  for V1 being Subspace of V, W1 being Subspace of V1, v being
  VECTOR of V st v in W1 holds v is VECTOR of V1
proof
  let V1 be Subspace of V, W1 be Subspace of V1, v be VECTOR of V;
  assume v in W1;
  then the carrier of W1 c= the carrier of V1 & v in the carrier of W1 by
RLSUB_1:def 2;
  hence thesis;
end;
