theorem :: JORDAN6:52

for P being Subset of (TOP-REAL 2)
for P1 being Subset of ((TOP-REAL 2) | P) st P is being_simple_closed_curve & (Upper_Arc P) /\ P1 = {(W-min P),(E-max P)} & (Upper_Arc P) \/ P1 = P holds
P1 = Lower_Arc P