proposition: Lemma cut_comm : forall A B l, cut l A B -> cut l B A.
proof: Proof. intros. unfold cut in *. spliter. repeat split; auto. destruct H1 as [I H1]. exists I. spliter. apply between_comm in H2. split; 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