proposition: Lemma par__or_eq_para : forall A B C D l m, IncidL A l -> IncidL B l -> IncidL C m -> IncidL D m -> Par A B C D -> Para l m \/ EqL l m.
proof: Proof. intros A B C D l m HA HB HC HD [HParS|Heq]. left; apply (pars__para A B C D); assumption. right. spliter. rewrite col_colh in *. apply (line_uniqueness A B); trivial; apply (colH_IncidL__IncidL C D); Col. 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