(** 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 not_aah :
hypothesis_of_right_saccheri_quadrilaterals \/ hypothesis_of_obtuse_saccheri_quadrilaterals -> ~ hypothesis_of_acute_saccheri_quadrilaterals.