theorem Th1: :: INTEGR11:1

( (AffineMap ((1 / 2),0)) - ((1 / 4) (#) (sin * (AffineMap (2,0)))) is_differentiable_on REAL & ( for x being Real holds (((AffineMap ((1 / 2),0)) - ((1 / 4) (#) (sin * (AffineMap (2,0))))) `| REAL) . x = (sin . x) ^2 ) )