proposition: Lemma le_lt_per2__lt : forall A B C A' B' C', Per A B C -> Per A' B' C' -> Le A B A' B' -> Lt B C B' C' -> Lt A C A' C'.
proof: Proof. intros. destruct (cong_dec A B A' B'). apply cong_lt_per2__lt with B B'; assumption. assert (Lt A B A' B') by (split; assumption). apply lt2_per2__lt with B B'; assumption. Qed.
imports: GeoCoq.Tarski_dev.Ch10_line_reflexivity_2