unfold outH in H.
induction H.
apply between_col in H.
auto.
induction H.
apply between_col in H.
Col.
spliter.
subst C.
Col.
Qed.

Lemma IncidLP_morphism : forall l m p q, IncidLP l p -> EqL l m -> EqP p q -> IncidLP m q.
Global Instance IncidLP_morphisml : Proper(EqL ==> eq ==> iff) IncidLP.