theorem :: FDIFF_11:5

for Z being open Subset of REAL st Z c= dom (arctan * tan) & ( for x being Real st x in Z holds
( tan . x > - 1 & tan . x < 1 ) ) holds
( arctan * tan is_differentiable_on Z & ( for x being Real st x in Z holds
((arctan * tan) `| Z) . x = 1 ) )