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