proposition: Lemma axiom_between_one : forall A B C, A<>B -> A<>C -> B<>C -> Col_H A B C -> Between_H A B C \/ Between_H B C A \/ Between_H B A C.
proof: Proof. intros. apply between_one;try assumption. apply cols_coincide_1. assumption. 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