proposition: Lemma lemma_lessthannotequal : forall A B C D, Lt A B C D -> neq A B /\ neq C D.
proof: Proof. intros. let Tf:=fresh in assert (Tf:exists E, (BetS C E D /\ Cong C E A B)) by (conclude_def Lt );destruct Tf as [E];spliter. assert (neq C E) by (forward_using lemma_betweennotequal). assert (neq A B) by (conclude axiom_nocollapse). assert (neq C D) by (forward_using lemma_betweennotequal). close. Qed.
imports: GeoCoq.Elements.OriginalProofs.lemma_betweennotequal