Require Export GeoCoq.Tarski_dev.Ch12_parallel_inter_dec.
Section Orientation.
Context `{T2D:Tarski_2D}.
Context `{TE:@Tarski_euclidean Tn TnEQD}.
Definition proj := fun  T A B P => A <> B /\ (~Col A B T /\ Perp A B T P /\ Col A B P \/ Col A B T /\ P = T).

(* Specifications: *)
Lemma proj_exists : forall A B T, A <> B -> exists P, proj T A B P.
intros.