theorem :: JORDAN6:53

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