proposition: Lemma bet_trans: forall A B C D : Point, Bet A B D -> Bet B C D -> Bet A B C.
proof: Proof. unfold Bet. intros. destruct H as [|[|]]; destruct H0 as [|[|]]; subst; auto. left. apply between_comm. apply (betH_trans0 D C B A); Bet. exfalso. apply (between_diff D C D); trivial. 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