(** 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_17__rah : forall A B C M, ~ Col A B C -> Midpoint M A B -> Cong M A M C -> (Per A C B <-> hypothesis_of_right_saccheri_quadrilaterals).