proposition: Lemma col_colh : forall A B C, Col A B C <-> ColH A B C.
proof: Proof. unfold Col. intros A B C; split; intro HCol. destruct HCol as [H|[H|H]]; apply bet_colH in H; Col. apply ColH_bets, HCol. 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