theorem :: FDIFF_9:22

for Z being open Subset of REAL st Z c= dom (sec - (id Z)) holds
( sec - (id Z) is_differentiable_on Z & ( for x being Real st x in Z holds
((sec - (id Z)) `| Z) . x = ((sin . x) - ((cos . x) ^2)) / ((cos . x) ^2) ) )