proposition: Lemma ColH_bets : forall A B C, ColH A B C -> Bet A B C \/ Bet B C A \/ Bet C A B.
proof: Proof. intros. induction (eq_dec_pointsH A B). subst;unfold Bet;auto. induction (eq_dec_pointsH B C). subst;unfold Bet;auto. induction (eq_dec_pointsH A C). subst;unfold Bet;auto. apply between_one in H;try assumption. unfold Bet. decompose [or] H;auto using between_comm. 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