Section Tarski_is_a_Coinc_theory_for_concyclic.
Context `{TE:Tarski_euclidean}.
Definition not_col : arity Tpoint 3 := fun A B C : Tpoint => ~ Col A B C.

(* Specifications: *)
Lemma not_col_perm_1 : forall A X, app_1_n not_col A X -> app_n_1 not_col X A.
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).