proposition: Lemma same_side_not_incid : forall A B l, same_side A B l -> ~ IncidL A l /\ ~ IncidL B l.
proof: Proof. intros. unfold same_side in *. destruct H as [P [HP1 HP2]]. unfold cut in *. spliter;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