(** 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 *)

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'.