proposition: Lemma bet_colH : forall A B C, Bet A B C -> ColH A B C.
proof: Proof. intros. unfold Bet in H. induction H. apply between_col in H. spliter. assumption. induction H;subst B. apply colH_trivial112. apply colH_trivial122. 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