Definition is_line A B l := A <> B /\ IncidL A l /\ IncidL B l.

(* Specifications: *)
Lemma cut_exists : forall A l, ~IncidL A l -> exists B, cut l A B.
Lemma outH_col : forall A B C, outH A B C -> ColH A B C.
Lemma cut_distinct : forall A B l, cut l A B -> A <> B.
Lemma same_side_not_cut : forall A B l, same_side A B l -> ~cut l A B.
Lemma IncidLP_morphism : forall l m p q, IncidLP l p -> EqL l m -> EqP p q -> IncidLP m q.