(** If the angles ACB and ADB are congruent and C, D lie on the same side of AB, then A, B, C and D are concyclic. *)

Lemma conga_os__ex_circle : forall A B C D,
OS A B C D -> CongA 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.