Require Export GeoCoq.Elements.OriginalProofs.lemma_collinear4.
Section Euclid.
Context `{Ax1:euclidean_neutral_ruler_compass}.

(* Specifications: *)
Lemma lemma_oppositesidesymmetric :
forall A B P Q,
TS P A B Q ->
TS Q A B P.
Lemma lemma_twolines2 :
forall A B C D P Q,
neq A B -> neq C D -> Col P A B -> Col P C D -> Col Q A B -> Col Q C D -> ~ (Col A C D /\ Col B C D) ->
eq P Q.
Lemma lemma_twolines :
forall A B C D E F,
Cut A B C D E -> Cut A B C D F -> nCol B C D ->
eq E F.
Lemma lemma_Pasch_outer2 :
forall A B C P Q,
BetS A P C -> BetS B C Q -> nCol B P A ->
exists X, BetS A X Q /\ BetS B P X.