proposition: Lemma same_side_prime_refl: forall A B C, ~ ColH A B C -> same_side' C C A B.
proof: Proof. intros. unfold same_side'. split. apply ncolH_distincts in H;intuition. intros. apply same_side_refl. intro. apply H. exists l;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