for P, P1, P2, P19, P29 being Subset of (TOP-REAL 2)
for p1, p2 being Point of (TOP-REAL 2) st P is being_simple_closed_curve & P1 is_an_arc_of p1,p2 & P2 is_an_arc_of p1,p2 & P1 \/ P2 = P & P19 is_an_arc_of p1,p2 & P29 is_an_arc_of p1,p2 & P19 \/ P29 = P & not ( P1 = P19 & P2 = P29 ) holds
( P1 = P29 & P2 = P19 )