theorem :: JORDAN16:14

for C being Simple_closed_curve
for A1, A2 being Subset of (TOP-REAL 2)
for p1, p2 being Point of (TOP-REAL 2) st A1 c= C & A2 c= C & A1 <> A2 & A1 is_an_arc_of p1,p2 & A2 is_an_arc_of p1,p2 holds
for A being Subset of (TOP-REAL 2) st A is_an_arc_of p1,p2 & A c= C & not A = A1 holds
A = A2