reserve X for set,
        n,m,k for Nat,
        K for Field,
        f for n-element real-valued FinSequence,
        M for Matrix of n,m,F_Real;

theorem
  for Af be Subset of n-VectSp_over F_Real,
      Ar be Subset of REAL-NS n st Af = Ar
  holds [#]Lin Ar = [#]Lin Af
  proof
    let Af be Subset of n-VectSp_over F_Real,
        Ar be Subset of REAL-NS n;
    assume
    A1: Af = Ar;
    reconsider At = Ar as Subset of TOP-REAL n by Th4;
    [#]Lin At = [#]Lin Ar by Th26;
    hence thesis by MATRTOP2:6,A1;
  end;
