Section triangle_playfair_bis.
Context `{TnEQD:Tarski_neutral_dimensionless_with_decidable_point_equality}.

Lemma legendre_aux :
greenberg_s_axiom ->
triangle_postulate ->
forall A B C P Q,
Perp Q A P Q -> Perp P B P Q -> Par_strict Q A P B ->
Par_strict Q A P C -> OS P B Q C -> OS P Q C A -> OS P Q C B ->
False.