proposition: Lemma congH_permlr : forall A B C D, A<>B -> C<>D -> CongH A B C D -> CongH B A D C.
proof: Proof. intros. apply cong_pseudo_transitivity with A B. apply congH_perm. auto. apply cong_pseudo_transitivity with C D. apply congH_sym. assumption. assumption. apply congH_perm. assumption. 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