theorem :: SPPOL_2:59

for P being Subset of (TOP-REAL 2) st P is special_polygonal holds
for p1, p2 being Point of (TOP-REAL 2) st p1 <> p2 & p1 in P & p2 in P holds
ex P1, P2 being Subset of (TOP-REAL 2) st
( P1 is_S-P_arc_joining p1,p2 & P2 is_S-P_arc_joining p1,p2 & P1 /\ P2 = {p1,p2} & P = P1 \/ P2 )