Require Export GeoCoq.Meta_theory.Parallel_postulates.parallel_postulates.
Require Export GeoCoq.Meta_theory.Parallel_postulates.par_trans_NID.
Section T13.
Context `{TE:Tarski_euclidean}.

Lemma parallel_uniqueness :
forall A1 A2 B1 B2 C1 C2 P : Tpoint,
Par A1 A2 B1 B2 -> Col P B1 B2 ->
Par A1 A2 C1 C2 -> Col P C1 C2 ->
Col C1 B1 B2 /\ Col C2 B1 B2.