proposition: Lemma addition_betH : forall A B C A' B' C', BetH A B C -> BetH A' B' C' -> CongH A B A' B' -> CongH B C B' C' -> CongH A C A' C'.
proof: Proof. intros. apply addition with B B';auto using bet_disjoint, between_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