proposition: Lemma cong_inner_transitivity : forall A B C D E F, Cong A B C D -> Cong A B E F -> Cong C D E F.
proof: Proof. intros. unfold Cong in *. induction H. induction H0. spliter. left. repeat split; auto. apply (cong_pseudo_transitivity A B); auto. spliter. contradiction. induction H0. spliter. contradiction. right. 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