proposition: Lemma between_only_one' : forall A B C, BetH A B C -> ~ BetH B C A /\ ~ BetH B A C.
proof: Proof. intros A B C HBet1; assert (HBet2 := between_comm _ _ _ HBet1). split; apply between_only_one; 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