Section Legendre.
Context `{TnEQD:Tarski_neutral_dimensionless_with_decidable_point_equality}.

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').