(** Saccheri's three hypotheses *)

Definition hypothesis_of_right_saccheri_quadrilaterals := forall A B C D, Saccheri A B C D -> Per A B C.Definition hypothesis_of_acute_saccheri_quadrilaterals := forall A B C D, Saccheri A B C D -> Acute A B C.Definition hypothesis_of_obtuse_saccheri_quadrilaterals := forall A B C D, Saccheri A B C D -> Obtuse A B C.

Lemma t22_14__bet_aux : forall A B C P Q R, hypothesis_of_right_saccheri_quadrilaterals -> ~ Col A B C -> TriSumA A B C P Q R -> Acute A B C -> Acute A C B -> Bet P Q R.