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 concyclic_gen_pseudo_trans : forall A B C D P Q R, ~ Col P Q R -> Concyclic_gen P Q R A -> Concyclic_gen P Q R B -> Concyclic_gen P Q R C -> Concyclic_gen P Q R D -> Concyclic_gen A B C D.