(** The following development is inspired by The Foundations of Geometry and the Non-Euclidean Plane, by George E Martin, chapter 22 *)

Lemma t22_16_2aux :
~ hypothesis_of_obtuse_saccheri_quadrilaterals ->
forall A B C D A1 A2 A3 B1 B2 B3 C1 C2 C3 D1 D2 D3 O P Q R,
Defect A B C D1 D2 D3 -> Defect A B D C1 C2 C3 ->
Defect A D C B1 B2 B3 -> Defect C B D A1 A2 A3 ->
Bet A O C -> Bet B O D -> Col A B C -> SumA D1 D2 D3 B1 B2 B3 P Q R ->
SAMS C1 C2 C3 A1 A2 A3 /\ SumA C1 C2 C3 A1 A2 A3 P Q R.