proposition: Lemma betH2_out : forall A B C D, B <> C -> BetH A B D -> BetH A C D -> BetH A B C \/ BetH A C B.
proof: Proof. intros. apply betH_expand in H0. apply betH_expand in H1. spliter. assert(ColH A B C). apply (colH_trans A D); Col. apply between_one in H10; auto. induction H10. left; auto. induction H10. right; Bet. assert(BetH C A D /\ BetH C B D). apply(betH_trans C A B D); Bet. induction H11. apply between_only_one' in H11. spliter. contradiction. 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