proposition: Lemma other_point_on_line : forall A l, IncidL A l -> exists B, A <> B /\ IncidL B l.
proof: Proof. intros. assert(HH:= two_points_on_line l). destruct HH as [X HH]. destruct HH as [Y HH]. spliter. induction(eq_dec_pointsH A X). exists Y. subst X. split; auto. exists X. split; auto. 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