(** 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_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).