theorem
  for Lv be Linear_Combination of n-VectSp_over F_Real,
      Lr be Linear_Combination of REAL-NS n
    st Lr = Lv
  holds Carrier Lr = Carrier Lv
  proof
    let Lv be Linear_Combination of n-VectSp_over F_Real,
        Lr be Linear_Combination of REAL-NS n;
    assume
    A1: Lr = Lv;
    reconsider Lr1 = Lr as Linear_Combination of TOP-REAL n by Th11;
    Carrier Lr1 = Carrier Lv by A1, MATRTOP2:2;
    hence thesis;
  end;
