(** First case of congruence of triangles *)

(* Specifications: *)
Lemma th12: forall A B C A' B' C',
~ ColH A B C ->
~ ColH A' B' C' ->
CongH A B A' B' ->
CongH A C A' C' ->
CongaH B A C B' A' C' ->
CongaH A B C A' B' C' /\ CongaH A C B A' C' B' /\ CongH B C B' C'.
Lemma th14: forall A B C D A' B' C' D',
~ ColH A B C ->
~ ColH A' B' C' ->
CongaH A B C A' B' C' ->
BetH A B D ->
BetH A' B' D' ->
CongaH C B D C' B' D'.
Lemma congH_colH_betH: forall A B I,
A<>B -> A<>I -> B<>I ->
CongH I A I B ->
ColH I A B ->
BetH A I B.