reserve n   for Nat,
        r,s for Real,
        x,y for Element of REAL n,
        p,q for Point of TOP-REAL n,
        e   for Point of Euclid n;
reserve n for non zero Nat;
reserve n for non zero Nat;
reserve n for Nat,
        X for set,
        S for Subset-Family of X;
reserve n for Nat,
        S for Subset-Family of REAL;
reserve n       for Nat,
        a,b,c,d for Element of REAL n;
reserve n for non zero Nat;
reserve n     for non zero Nat,
        x,y,z for Element of REAL n;

theorem
  the RLSStruct of TOP-REAL n = the RLSStruct of TOP-REAL-INFTY n
  proof
    the RLSStruct of TOP-REAL n = RealVectSpace Seg n by EUCLID:def 8;
    hence thesis by Def8;
  end;
