proposition: Lemma tarski_s_euclid : tarski_s_parallel_postulate.
proof: Proof. cut playfair_s_postulate; [|apply playfair_s_postulateH]. assert (H := equivalent_postulates_with_decidability_of_intersection_of_lines). apply (H decidability_of_intersectionH); simpl; tauto. 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 GeoCoq.Meta_theory.Parallel_postulates.parallel_postulates