proposition: Lemma Perp_in_perm : forall X A B C D, Perp_at X A B C D -> Perp_at X A B C D /\ Perp_at X B A C D /\ Perp_at X A B D C /\ Perp_at X B A D C /\ Perp_at X C D A B /\ Perp_at X C D B A /\ Perp_at X D C A B /\ Perp_at X D C B A.
proof: Proof. intros. do 7 (split; Perp). Qed.
imports: GeoCoq.Tarski_dev.Ch07_midpoint GeoCoq.Tactics.Coinc.ColR