Require Export GeoCoq.Elements.OriginalProofs.lemma_3_7a.

Section Euclid.

Context `{Ax:euclidean_neutral_ruler_compass}.

Lemma lemma_3_7b : 
   forall A B C D, 
   BetS A B C -> BetS B C D ->
   BetS A B D.
Proof.
(* Goal: forall (A B C D : @Point Ax0) (_ : @BetS Ax0 A B C) (_ : @BetS Ax0 B C D), @BetS Ax0 A B D *)
intros.
(* Goal: @BetS Ax0 A B D *)
assert (BetS C B A) by (conclude axiom_betweennesssymmetry).
(* Goal: @BetS Ax0 A B D *)
assert (BetS D C B) by (conclude axiom_betweennesssymmetry).
(* Goal: @BetS Ax0 A B D *)
assert (BetS D B A) by (conclude lemma_3_7a).
(* Goal: @BetS Ax0 A B D *)
assert (BetS A B D) by (conclude axiom_betweennesssymmetry).
(* Goal: @BetS Ax0 A B D *)
close.
Qed.

End Euclid.


