for P being Subset of (TOP-REAL 2)
for p1, p2, q1, q2 being Point of (TOP-REAL 2) st P is_an_arc_of p1,p2 & q1 in P & q2 in P & q1 <> p1 & q1 <> p2 & q2 <> p1 & q2 <> p2 & q1 <> q2 holds
ex Q being non empty Subset of (TOP-REAL 2) st
( Q is_an_arc_of q1,q2 & Q c= P & Q misses {p1,p2} )