Library GeoCoq.Elements.OriginalProofs.lemma_ray2

Require Export GeoCoq.Elements.OriginalProofs.lemma_betweennotequal.

Section Euclid.

Context `{Ax:euclidean_neutral}.

Lemma lemma_ray2 :
   ∀ A B C,
   Out A B C →
   neq A B.
Proof.
intros.
let Tf:=fresh in
assert (Tf:∃ E, (BetS E A C ∧ BetS E A B)) by (conclude_def Out );destruct Tf as [E];spliter.
assert (neq A B) by (forward_using lemma_betweennotequal).
close.
Qed.

End Euclid.