proposition: Lemma colH_trans : forall X Y A B C, X <> Y -> ColH X Y A -> ColH X Y B -> ColH X Y C -> ColH A B C.
proof: Proof. intros. destruct H0 as [l]. destruct H1 as [m]. destruct H2 as [o]. exists l. spliter. repeat split. assumption. rewrite (line_uniqueness X Y l m); assumption. rewrite (line_uniqueness X Y l o); assumption. 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