proposition: Lemma other_point_exists : forall A: Point, exists B, A <> B.
proof: Proof. intros. assert (T:=lower_dim_2). destruct T. induction(eq_dec_pointsH A PP). subst A. exists PQ. intuition. exists PP. 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