for a, b, c, d being Real
for f being Function of (Closed-Interval-TSpace (a,b)),(Closed-Interval-TSpace (c,d))
for g being PartFunc of REAL,REAL st f is continuous & f is one-to-one & a < b & c < d & f = g & f . a = c & f . b = d holds
g | [.a,b.] is continuous