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.

(* Specifications: *)
Lemma concyclic_gen_2341 : forall A B C D, Concyclic_gen A B C D -> Concyclic_gen B C D A.
Lemma concy_perm_1 : forall (A : Tpoint) (X : cartesianPower Tpoint 3), app_1_n concy A X -> app_n_1 concy X A.
Lemma concyclic_gen_2134 : forall A B C D, Concyclic_gen A B C D -> Concyclic_gen B A C D.
Lemma concy_perm_2 : forall (A B : Tpoint) (X : cartesianPower Tpoint 2), app_2_n concy A B X -> app_2_n concy B A X.
Lemma concyclic_gen_1123 : forall A B C, Concyclic_gen A A B C.
Lemma concy_bd : forall (A : Tpoint) (X : cartesianPower Tpoint 2), app_2_n concy A A X.
Lemma concy_trans_1 : forall P Q R A B, ~Col P Q R -> Concyclic_gen P Q R A -> Concyclic_gen P Q R B -> Concyclic_gen Q R A B.
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.
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.