Section Legendre.
Context `{TnEQD:Tarski_neutral_dimensionless_with_decidable_point_equality}.

Lemma legendre_aux :
~ hypothesis_of_obtuse_saccheri_quadrilaterals ->
forall A B C D B1 C1 P Q R S T U V W X,
~ Col A B C -> CongA A C B C B D ->
Cong A C B D -> TS B C A D -> Out A B B1 -> Out A C C1 -> Bet B1 D C1 ->
Defect A B C P Q R -> Defect A B1 C1 S T U -> SumA P Q R P Q R V W X ->
SAMS P Q R P Q R /\ LeA V W X S T U.