Lemma legendre_aux2 : ~ hypothesis_of_obtuse_saccheri_quadrilaterals -> forall A B C, ~ Col A B C -> Acute B A C -> (forall T, InAngle T B A C -> exists X Y : Tpoint, Out A B X /\ Out A C Y /\ Bet X T Y) -> forall P Q R S T U, Defect A B C P Q R -> GradAExp P Q R S T U -> exists B' C' P' Q' R', (Out A B B' /\ Out A C C' /\ Defect A B' C' P' Q' R' /\ LeA S T U P' Q' R').