proposition: Lemma EqL_dec : forall l m, EqL l m \/ ~EqL l m.
proof: Proof. intros. assert(HH:=two_points_on_line l). ex_and HH A. ex_and p B. induction(IncidL_dec A m). induction(IncidL_dec B m). left. lines_eq l m. auto. right. intro. apply H3. rewrite <-H4. assumption. induction(IncidL_dec B m). right. intro. apply H2. rewrite <-H4. auto. right. intro. rewrite <-H4 in H2. contradiction. 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