proposition: Lemma cols_coincide : forall A B C, Col A B C <-> Col_H A B C.
proof: Proof. intros. split. apply cols_coincide_2. apply cols_coincide_1. 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