Section Saccheri.
Context `{TnEQD:Tarski_neutral_dimensionless_with_decidable_point_equality}.
(** The two following lemmas come from Theorem 21.10 *)
(** The five following lemmas come from Theorem 21.8 *)
(** The two following lemmas constitute Theorem 21.11 *)
(** The four following constitute Theorem 22.3 *)
(** The six following lemmas constitute Theorem 22.5 *)
(** The three following lemmas constitute Omar Khayyam's Theorem (22.6) *)

Lemma t22_8_aux : forall A B C D R S J,
Saccheri A B C D -> Bet B C R -> Bet A D S -> D <> S -> Per A S R ->
Out S R J -> Cong S J A B ->
C <> R /\ Saccheri A B J S /\ Saccheri D C J S /\ OS S J C B /\ Coplanar A B C J.