proposition: Lemma outH_out : forall P A B, outH P A B -> Out P A B.
proof: Proof. unfold outH. unfold Out. intros. induction H. unfold Between_H in H. spliter. repeat split; auto. induction H. unfold Between_H in H. spliter. repeat split; auto. spliter. repeat split. auto. subst B. auto. subst B. left. apply between_trivial. Qed.
imports: Morphisms GeoCoq.Axioms.hilbert_axioms GeoCoq.Axioms.parallel_postulates GeoCoq.Meta_theory.Parallel_postulates.tarski_playfair GeoCoq.Meta_theory.Parallel_postulates.SPP_ID GeoCoq.Meta_theory.Dimension_axioms.upper_dim_3 GeoCoq.Meta_theory.Parallel_postulates.parallel_postulates GeoCoq.Utils.triples