theorem Th52:
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)))) &
rng f c= closed_inside_of_rectangle (
a,
b,
c,
d) holds
rng (h * f) c= closed_inside_of_rectangle (
(- 1),1,
(- 1),1)