(** 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__sams_nbet : hypothesis_of_acute_saccheri_quadrilaterals -> forall A B C D E F P Q R, ~ Col A B C -> SumA C A B A B C D E F -> SumA D E F B C A P Q R -> SAMS D E F B C A /\ ~ Bet P Q R.