proposition: Lemma betH_outH__outH : forall A B C D, BetH A B C -> outH B C D -> outH A C D.
proof: Proof. intros. destruct H0. unfold outH. left. apply (betH_trans A B C D);auto. destruct H0. unfold outH. right;left. apply between_comm; apply (betH_trans0 C D B A);auto using between_comm. spliter. subst. apply outH_trivial. apply betH_expand in H;spliter;auto. Qed.
imports: Setoid Coq.Classes.Morphisms Coq.Classes.Morphisms_Prop GeoCoq.Axioms.gupta_inspired_variant_axioms GeoCoq.Meta_theory.Models.gupta_inspired_to_tarski GeoCoq.Tactics.Coinc.tactics_axioms GeoCoq.Tactics.Coinc.ColR GeoCoq.Meta_theory.Dimension_axioms.upper_dim_3 GeoCoq.Meta_theory.Parallel_postulates.parallel_postulates GeoCoq.Axioms.hilbert_axioms