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) *)
(** The two following lemmas come from Theorem 22.4 *)
(** This comes from Martin's proof in Theorem 22.10 *)

Lemma three_hypotheses_aux : forall A B C D M N A' B' C' D' M' N',
Saccheri A B C D -> Saccheri A' B' C' D' ->
Midpoint M B C -> Midpoint M' B' C' -> Midpoint N A D -> Midpoint N' A' D' ->
Le M N M' N' ->
(Per A B C <-> Per A' B' C') /\ (Acute A B C <-> Acute A' B' C').