proposition: Lemma proj_id : forall A B A' B' P Q, A <> A' -> Col A B A' -> proj A P Q A' -> proj B P Q B' -> A'= B'.
proof: Proof. intros. assert(proj B P Q A'). eapply col_proj_proj. apply H. assumption. assumption. eapply proj_uniqueness. apply H3. assumption. Qed.
imports: GeoCoq.Tarski_dev.Ch12_parallel_inter_dec