Require Export GeoCoq.Elements.OriginalProofs.lemma_ray1.
Require Export GeoCoq.Elements.OriginalProofs.lemma_raystrict.
Require Export GeoCoq.Elements.OriginalProofs.lemma_ray4.

Section Euclid.

Context `{Ax:euclidean_neutral_ruler_compass}.

Lemma lemma_ray5 : 
   forall A B C, 
   Out A B C ->
   Out A C B.
Proof.
(* Goal: forall (A B C : @Point Ax0) (_ : @Out Ax0 A B C), @Out Ax0 A C B *)
intros.
(* Goal: @Out Ax0 A C B *)
assert ((BetS A C B \/ eq B C \/ BetS A B C)) by (conclude lemma_ray1).
(* Goal: @Out Ax0 A C B *)
assert (neq A C) by (conclude lemma_raystrict).
(* Goal: @Out Ax0 A C B *)
assert (Out A C B) by (conclude lemma_ray4).
(* Goal: @Out Ax0 A C B *)
close.
Qed.

End Euclid.


