theorem :: JORDAN16:22

for C being Simple_closed_curve
for p1, p2 being Point of (TOP-REAL 2)
for P being Subset of (TOP-REAL 2) st P c= C & P is_an_arc_of p1,p2 & W-min C in P & E-max C in P & not Upper_Arc C c= P holds
Lower_Arc C c= P