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 *)

Lemma mid2_sac__perp_lower : forall A B C D M N,
Saccheri A B C D ->
Midpoint M B C -> Midpoint N A D ->
Perp A D M N.