proposition: Lemma betH_trans : forall A B C D, BetH A B C -> BetH B C D -> BetH A B D /\ BetH A C D.
proof: Proof. intros. split. apply (betH_trans2 A B C D); auto. apply (betH_trans1 A B C D); 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