proposition: Lemma Plg_perm : forall A B C D, Parallelogram A B C D -> Parallelogram A B C D /\ Parallelogram B C D A /\ Parallelogram C D A B /\Parallelogram D A B C /\ Parallelogram A D C B /\ Parallelogram D C B A /\ Parallelogram C B A D /\ Parallelogram B A D C.
proof: Proof. intros. split; try assumption. split; try (apply plg_permut; assumption). split; try (do 2 apply plg_permut; assumption). split; try (do 3 apply plg_permut; assumption). split; try (apply plg_comm2; do 3 apply plg_permut; assumption). split; try (apply plg_comm2; do 2 apply plg_permut; assumption). split; try (apply plg_comm2; apply plg_permut; assumption). apply plg_comm2; assumption. Qed.
imports: GeoCoq.Tarski_dev.Ch12_parallel_inter_dec GeoCoq.Tarski_dev.Annexes.Tagged_predicates