Variable R : rcfType.Definition point := (@Vector R 1).

Global Instance Rcf_to_IT_PED :er_dim R)).
Defined.ski_neutral_dimensionless.
Proof. apply TG_to_T. Defined.

Global Instance Rcf_to_T_PED :_to_T.
Proof. split; exact (@point_equality_decidability R 1). Defined._variant_of_Tarski_2D Rcf_to_IT_PED.
Proof. split; exact (@upper_dim R). Defined.cf_to_T_PED.
Proof. split; exact upper_dimT. Defined._inspired_variant_of_Tarski_euclidean Rcf_to_IT_PED.
Proof. split; exact (@euclid R 1). Defined.Implicit Types (a b c d p q : point).Definition col a b c := bet a b c \/ bet b c a \/ bet c a b.

Definition coplanar a b c d :=
  exists x, (col a b x /\ col c d x) \/
            (col a c x /\ col b d x)\/
            (col a d x /\ col b c x).

Definition par_strict a b c d :=a <> b /\ c <> d /\ coplanar a b c d /\ ~ exists x, col x a b /\ col x c d.

Definition par a b c d :=

(* Specifications: *)
Lemma proclus a b c d p q : par a b c d -> col a b p -> ~ col