Definition Concyclic_gen A B C D :=
  Concyclic A B C D \/ (Col A B C /\ Col A B D /\ Col A C D /\ Col B C D).Definition concy : arity Tpoint 4 := Concyclic_gen.

Lemma concy_3 : forall (CONCY : cartesianPower Tpoint 4) (NOT_COL : cartesianPower Tpoint 3), pred_conj concy CONCY NOT_COL -> app not_col NOT_COL -> app concy CONCY.