theorem Th53: :: JGRAPH_7:53

for a, b, c, d being Real
for h being Function of (TOP-REAL 2),(TOP-REAL 2)
for f being Function of I[01],(TOP-REAL 2) st a < b & c < d & h = AffineMap ((2 / (b - a)),(- ((b + a) / (b - a))),(2 / (d - c)),(- ((d + c) / (d - c)))) & f is continuous & f is one-to-one holds
( h * f is continuous & h * f is one-to-one )