Definition cop : arity Tpoint 4 := Coplanar.

(* Specifications: *)
Lemma cop_perm_1 : forall A (X : cartesianPower Tpoint 3), app_1_n cop A X -> app_n_1 cop X A.
Lemma cop_perm_2 : forall A B (X : cartesianPower Tpoint 2), app_2_n cop A B X -> app_2_n cop B A X.
Lemma cop_bd : forall A (X : cartesianPower Tpoint 2), app_2_n cop A A X.
Lemma cop_3 : forall (COP : cartesianPower Tpoint 4) (NOT_COL : cartesianPower Tpoint 3), pred_conj cop COP NOT_COL -> app not_col NOT_COL -> app cop COP.