Proof with Geometry.
unfold inter_ll in |- *.
intros.
intuition.
Qed.
Hint Resolve inter_ll_comm1 inter_ll_comm2 inter_ll_comm3 inter_ll_comm4: Geom.

Theorem aux_co_side_2 :
forall A B P Q M : Point, P <> M -> inter_ll M A B P Q -> S P A B <>0.