proposition: Lemma colH_dec : forall A B C, ColH A B C \/ ~ ColH A B C.
proof: Proof. intros. induction(eq_dec_pointsH A B). subst B. left. apply colH_trivial112. destruct (line_existence A B H) as [l []]. induction(IncidL_dec C l). left. exists l. repeat split; assumption. right. intro. apply H2. destruct H3 as [l00]; spliter. rewrite (line_uniqueness A B l l00 H); 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