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

Lemma t22_16_1bis :
~ hypothesis_of_obtuse_saccheri_quadrilaterals ->
forall A B C C1 D E F G H I K L M,
Bet A C1 C ->
Defect A B C1 D E F -> Defect B C1 C G H I -> Defect A B C K L M ->
SAMS D E F G H I /\ SumA D E F G H I K L M.