(** If the angles ACB and ADB are supplementary and C, D lie on opposite sides of AB, then A, B, C and D are concyclic. *)

Lemma suppa_ts__ex_circle : forall A B C D,
TS A B C D -> SuppA A C B A D B -> exists O P,
OnCircle A O P /\ OnCircle B O P /\ OnCircle C O P /\ OnCircle D O P /\ Coplanar A B C O.