proposition: Lemma bet_disjoint : forall A B C, BetH A B C -> disjoint A B B C.
proof: Proof. intros. unfold disjoint. intro. destruct H0 as [P []]. assert(HP:= betH_trans0 A P B C H0 H). spliter. apply between_only_one' in H1. 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