proposition: Lemma proj_id : forall A A', Proj A A' O E' E E' -> Col O E A -> Col O E A' -> A = O.
proof: Proof. intros. assert(HH:=grid_not_par). spliter. unfold Proj in H. spliter. induction H11. apply(l6_21 O E E' O); Col. assert(Col O A' A). apply(col_transitivity_1 _ E); Col. apply col_permutation_2. apply (col_transitivity_1 _ A'); Col. intro. subst A'. induction H11. apply H11. exists E. split; Col. spliter. contradiction. subst. apply(l6_21 O E E' O); Col. Qed.
imports: GeoCoq.Tarski_dev.Ch13_6_Desargues_Hessenberg