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.

(* 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.