reserve p,p1,p2,p3,p11,p22,q,q1,q2 for Point of TOP-REAL 2,
  f,h for FinSequence of TOP-REAL 2,
  r,r1,r2,s,s1,s2 for Real,
  u,u1,u2,u5 for Point of Euclid 2,
  n,m,i,j,k for Nat,
  N for Nat,
  x,y,z for set;
reserve lambda for Real;
reserve f for FinSequence of REAL;

theorem
  len f = n implies f in the carrier of TOP-REAL n
proof
  assume len f = n;
  then f in the carrier of Euclid n by Th45;
  hence thesis by Th8;
end;
