(** 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 absolute_exterior_angle_theorem : ~ hypothesis_of_obtuse_saccheri_quadrilaterals -> forall A B C D E F B', Bet B A B' -> A <> B' -> SumA A B C B C A D E F -> LeA D E F C A B'.