for P being non empty Subset of (TOP-REAL 2)
for p1, p2, q1, q2, q3 being Point of (TOP-REAL 2) st P is_an_arc_of p1,p2 & LE q1,q2,P,p1,p2 & LE q2,q3,P,p1,p2 holds
(Segment (P,p1,p2,q1,q2)) \/ (Segment (P,p1,p2,q2,q3)) = Segment (P,p1,p2,q1,q3)