for P being non empty Subset of (TOP-REAL 2)
for P1 being Subset of ((TOP-REAL 2) | P)
for Q being Subset of I[01]
for f being Function of I[01],((TOP-REAL 2) | P)
for s being Real st s >= 0 & P1 = { q0 where q0 is Point of (TOP-REAL 2) : ex ss being Real st
( s < ss & ss <= 1 & q0 = f . ss ) } & Q = ].s,1.] holds
f .: Q = P1