for P being Subset of (TOP-REAL 2)
for p1, p2, q1, q2 being Point of (TOP-REAL 2)
for g being Function of I[01],((TOP-REAL 2) | P)
for s1, s2 being Real st P is_an_arc_of p1,p2 & g is being_homeomorphism & g . 0 = p1 & g . 1 = p2 & g . s1 = q1 & 0 <= s1 & s1 <= 1 & g . s2 = q2 & 0 <= s2 & s2 <= 1 & s1 <= s2 holds
LE q1,q2,P,p1,p2