Require Export GeoCoq.Elements.OriginalProofs.lemma_samesidereflexive.
Require Export GeoCoq.Elements.OriginalProofs.lemma_sameside2.
Require Export GeoCoq.Elements.OriginalProofs.lemma_samesidesymmetric.
Require Export GeoCoq.Elements.OriginalProofs.proposition_12.
Require Export GeoCoq.Elements.OriginalProofs.lemma_8_7.
Section Euclid.
Context `{Ax:euclidean_neutral_ruler_compass}.

Lemma lemma_notperp :
forall A B C P,
BetS A C B -> nCol A B P ->
exists X, nCol A B X /\ OS X P A B /\ ~ Per A C X.