(** 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 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.