Require Export GeoCoq.Elements.OriginalProofs.lemma_congruenceflip.
Require Export GeoCoq.Elements.OriginalProofs.lemma_lessthancongruence.
Require Export GeoCoq.Elements.OriginalProofs.lemma_outerconnectivity.
Section Euclid.
Context `{Ax:euclidean_neutral_ruler_compass}.

(* Specifications: *)
Lemma lemma_trichotomy1 :
forall A B C D,
~ Lt A B C D -> ~ Lt C D A B -> neq A B -> neq C D ->
Cong A B C D.