proposition: Lemma perp_in_col_perp_in : forall A B C D E P, C <> E -> Col C D E -> Perp_at P A B C D -> Perp_at P A B C E.
proof: Proof. intros. unfold Perp_at in *. spliter. repeat split; auto. ColR. intros. apply H5. assumption. ColR. Qed.
imports: GeoCoq.Tarski_dev.Ch07_midpoint GeoCoq.Tactics.Coinc.ColR