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

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.