for n being Element of NAT
for p1, p2 being Point of (TOP-REAL n)
for P being Subset of (TOP-REAL n) st P is_an_arc_of p1,p2 holds
ex F being Path of p1,p2 ex f being Function of I[01],((TOP-REAL n) | P) st
( rng f = P & F = f )