proposition: Lemma betH_congH2__False : forall A B C A' B' C', BetH A B C -> BetH A' C' B' -> CongH A B A' B' -> CongH A C A' C' -> False.
proof: Proof. intros. apply betH_expand in H. apply betH_expand in H0. spliter. elim (segment_constructionH A' B' B C);auto. intros C0 [HA HB]. assert (CongH A' C0 A C) by (apply addition_betH with B' B;auto using congH_sym). assert (BetH A' C' C0) by (apply (betH_trans0 A' C' B' C0);auto). apply betH_expand in H12; spliter. assert (CongH A' C' A' C0) by (apply cong_pseudo_transitivity with A C;auto using congH_sym). apply (betH_not_congH A' C' C0);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