reserve k,j,n for Nat,
  r for Real;
reserve x,x1,x2,y for Element of REAL n;
reserve f for real-valued FinSequence;
reserve p,p1,p2,p3 for Point of TOP-REAL n,
  x,x1,x2,y,y1,y2 for Real;
reserve p,p1,p2 for Point of TOP-REAL 2;

theorem
  for f being FinSequence of REAL holds
   f is Element of REAL len f & f is Point of TOP-REAL len f
proof
  let f be FinSequence of REAL;
  f is Element of REAL* by FINSEQ_1:def 11;
  then
  the carrier of TOP-REAL len f = the carrier of Euclid len f & f in ((len
  f) -tuples_on REAL) by Th39;
  hence thesis;
end;
