reserve n,i,k,m for Nat;
reserve r,r1,r2,s,s1,s2 for Real;
reserve p,p1,p2,q1,q2 for Point of TOP-REAL n;
reserve P,Q for Subset of TOP-REAL 2,
  f,f1,f2 for FinSequence of the carrier of TOP-REAL 2,
  p,p1,p2,p3,q,q3 for Point of TOP-REAL 2;

theorem
  for f holds {LSeg(f,i): 1<=i & i<=len f} is Subset-Family of TOP-REAL 2
proof
  let f;
  set F = {LSeg(f,i): 1<=i & i<=len f};
  F c= bool (REAL 2)
  proof
    let x be object;
    assume x in F;
    then ex i st LSeg(f,i)=x & 1<=i & i<=len f;
    then x is Subset of REAL 2 by EUCLID:22;
    hence thesis;
  end;
  hence thesis by EUCLID:22;
end;
