(** The three following lemmas link Saccheri's three hypotheses with triangles ABC having C on the circle of diameter AB; the first one states the equivalence between the Right angle hypothesis and Thales' theorem *)

(* Specifications: *)
Lemma t22_17__rah : forall A B C M,
~ Col A B C ->
Midpoint M A B -> Cong M A M C ->
(Per A C B <-> hypothesis_of_right_saccheri_quadrilaterals).
Lemma t22_17__oah : forall A B C M,
~ Col A B C ->
Midpoint M A B -> Cong M A M C ->
(Obtuse A C B <-> hypothesis_of_obtuse_saccheri_quadrilaterals).
Lemma t22_17__aah : forall A B C M,
~ Col A B C ->
Midpoint M A B -> Cong M A M C ->
(Acute A C B <-> hypothesis_of_acute_saccheri_quadrilaterals).
Lemma t22_20 : ~ hypothesis_of_obtuse_saccheri_quadrilaterals ->
forall A B C D E F, SumA A B C B C A D E F -> SAMS D E F C A B.
Lemma absolute_exterior_angle_theorem : ~ hypothesis_of_obtuse_saccheri_quadrilaterals ->
forall A B C D E F B', Bet B A B' -> A <> B' -> SumA A B C B C A D E F ->
LeA D E F C A B'.