proposition: Lemma ncols_coincide : forall A B C, ~ Col A B C <-> ~ Col_H A B C.
proof: Proof. intros. split; intros HNCol HCol; apply HNCol, cols_coincide, HCol. Qed.
imports: Morphisms GeoCoq.Axioms.hilbert_axioms GeoCoq.Axioms.parallel_postulates GeoCoq.Meta_theory.Parallel_postulates.tarski_playfair GeoCoq.Meta_theory.Parallel_postulates.SPP_ID GeoCoq.Meta_theory.Dimension_axioms.upper_dim_3 GeoCoq.Meta_theory.Parallel_postulates.parallel_postulates GeoCoq.Utils.triples