(** The sum of two angles of a triangle is less than a straight angle (three lemmas) *)

(* Specifications: *)
Lemma sams123231 : forall A B C, A <> B -> A <> C -> B <> C -> SAMS A B C B C A.
Lemma col_suma__col : forall A B C D E F, Col D E F -> SumA A B C B C A D E F -> Col A B C.
Lemma ncol_suma__ncol : forall A B C D E F, ~ Col A B C -> SumA A B C B C A D E F -> ~ Col D E F.
(** Sum of two right angles is a straight angle: 90+90=180. *)
Lemma per2_suma__bet : forall A B C D E F G H I, Per A B C -> Per D E F ->
SumA A B C D E F G H I -> Bet G H I.
Lemma bet_per2__suma : forall A B C D E F G H I,
A <> B -> B <> C -> D <> E -> E <> F -> G <> H -> H <> I ->
Per A B C -> Per D E F ->
Bet G H I -> SumA A B C D E F G H I.
Lemma per2__sams : forall A B C D E F, A <> B -> B <> C -> D <> E -> E <> F ->
Per A B C -> Per D E F -> SAMS A B C D E F.