(** 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_12__oah : forall A B C P Q R,
Per A B C -> SumA B C A C A B P Q R ->
(Obtuse P Q R <-> hypothesis_of_obtuse_saccheri_quadrilaterals).