for n being Element of NAT
for a, p1, p2 being Point of (TOP-REAL n)
for P being Subset of (TOP-REAL n) st a in P & P is_an_arc_of p1,p2 holds
ex f being Function of I[01],((TOP-REAL n) | P) ex r being Real st
( f is being_homeomorphism & f . 0 = p1 & f . 1 = p2 & 0 <= r & r <= 1 & f . r = a )