for a, b, d, e being Real st a <= b & e < 0 holds
ex f being Function of (Closed-Interval-TSpace (a,b)),(Closed-Interval-TSpace (((e * b) + d),((e * a) + d))) st
( f is being_homeomorphism & ( for r being Real st r in [.a,b.] holds
f . r = (e * r) + d ) )