BY-MO 2018 Problem 93

The bisector of angle $CAB$ of triangle $ABC$ intersects the side $CB$ at $L$ . The point $D$ is the foot of the perpendicular from $C$ to $AL$ and the point $E$ is the foot of perpendicular from $L$ to $AB$ . The lines $CB$ and $DE$ meet at $F$ . Prove that $AF$ is an altitude of triangle $ABC$ .