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

(* Specifications: *)
Lemma lemma_collinearbetween :
forall A B C D E F H,
Col A E B -> Col C F D -> neq A B -> neq C D -> neq A E -> neq F D -> ~ Meet A B C D -> BetS A H D -> Col E F H ->
BetS E H F.
Lemma lemma_collinearparallel :
forall A B C c d,
Par A B c d -> Col c d C -> neq C d ->
Par A B C d.
Lemma lemma_9_5a :
forall A B C P Q R,
TS P A B C -> BetS R P Q -> nCol R Q C -> Col A B R ->
TS Q A B C.
Lemma lemma_collinear5 :
forall A B C D E,
neq A B -> Col A B C -> Col A B D -> Col A B E ->
Col C D E.
Lemma lemma_9_5b :
forall A B C P Q R,
TS P A B C -> BetS R Q P -> nCol C P R -> Col A B R ->
TS Q A B C.
Lemma lemma_rayimpliescollinear :
forall A B C,
Out A B C ->
Col A B C.
Lemma lemma_paralleldef2A :
forall A B C D,
TP A B C D ->
Par A B C D.