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.

(* Specifications: *)
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.
Global Instance IncidLP_morphisml : Proper(EqL ==> eq ==> iff) IncidLP.
Lemma same_side_prime__plane : forall A B C D, same_side' A B C D ->
exists p, IncidP A p /\ IncidP B p /\ IncidP C p /\ IncidP D p.
Lemma cut_same_side_cut : forall P X Y l, cut l P X -> same_side X Y l -> cut l P Y.
(* Theorem 11 of Hilbert: the angles at the base of an isosceles triangle are congruent *)
Lemma isosceles_congaH : forall A B C, ~ColH A B C -> CongH A B A C -> CongaH A B C A C B.
Lemma cong_distincts : forall A B C D, A <> B -> Cong A B C D -> C <> D.
Lemma cong_sym : forall A B C D, Cong A B C D -> Cong C D A B.
intros.