reserve n for Element of NAT,
  V for Subset of TOP-REAL n,
  s,s1,s2,t,t1,t2 for Point of TOP-REAL n,
  C for Simple_closed_curve,
  P for Subset of TOP-REAL 2,
  a,p ,p1,p2,q,q1,q2 for Point of TOP-REAL 2;

theorem Th29:
  t1,s, V-separate s,t2
proof
  let A be Subset of TOP-REAL n such that
A1: A is_an_arc_of t1,s and
  A c= V;
A2: s in {s,t2} by TARSKI:def 2;
  s in A by A1,TOPREAL1:1;
  hence thesis by A2,XBOOLE_0:3;
end;
