proposition: Lemma betH_to_bet : forall A B C , BetH A B C -> Bet A B C /\ A <> B /\ B <> C /\ A <> C.
proof: Proof. intros. assert(HH:= betH_distincts A B C H). induction HH. split. unfold Bet. left. assumption. spliter. repeat split; assumption. 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