(* In this file we prove that Cop in Tarski neutral dimensionless is a Coinc_theory *)
Section Tarski_is_a_Coinc_theory_for_cop.
Context `{TnEQD:Tarski_neutral_dimensionless_with_decidable_point_equality}.
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.
Lemma not_col_perm_2 : forall A B (X : cartesianPower Tpoint 1),
app_2_n not_col A B X -> app_2_n not_col B A X.