  The cosection lemma proved by J. Li and Y.H. Kiem said the intrinsic normal
cone lies inside the kernel of any cosection of the obstruction sheaf when the
moduli has a perfect obstruction theory. With a definition of higher tangent
vectors of a scheme at a point, and a construction of the derived Kodaira
Spencer map by K. Behrend and B. Fantechi, we prove a derived version of
cosection lemma without perfect obstruction theory condition. As an application
we give a short proof of the Kodaira's Principle \textit{ambient cohomology
annihilates obstruction} (semiregularity), assuming the existence of locall
universal family.
