proposition: Lemma colH_trivial112 : forall A B, ColH A A B.
proof: Proof. intros. destruct (eq_dec_pointsH A B). subst. apply colH_trivial111. assert (H1:= line_existence A B H). decompose [ex and] H1. exists x. intuition. 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