proposition: Lemma vector_same_dir_cong : forall A B C D, A <> B -> C <> D -> exists X, exists Y, Same_dir A B X Y /\ Cong X Y C D.
proof: Proof. intros. exists A. assert(HH:=segment_construction_3 A B C D H H0). ex_and HH P. exists P. split; auto. unfold Same_dir. right. exists B. split. apply l6_6. assumption. apply eqv_refl. Qed.
imports: GeoCoq.Tarski_dev.Annexes.quadrilaterals_inter_dec