(** 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__rah : forall A B C,
A <> B -> B <> C -> Per A B C ->
(SumA B C A C A B A B C <-> hypothesis_of_right_saccheri_quadrilaterals).