for a, b, c, d, x1 being Real
for f being Function of (Closed-Interval-TSpace (a,b)),(Closed-Interval-TSpace (c,d))
for x being Point of (Closed-Interval-TSpace (a,b))
for g being PartFunc of REAL,REAL st a < b & c < d & f is_continuous_at x & f . a = c & f . b = d & f is one-to-one & f = g & x = x1 holds
g | [.a,b.] is_continuous_in x1