(** The three following lemmas constitute Omar Khayyam's Theorem (22.6) *)

Lemma t22_7__per : forall A B C D P Q,
Saccheri A B C D ->
Bet B P C -> Bet A Q D ->
A <> Q -> B <> P -> P <> C ->
Per P Q A ->
Cong P Q A B ->
Per A B C.