proposition: Lemma congH_perms : forall A B C D, A<>B -> C<>D -> CongH A B C D -> (CongH B A C D /\ CongH A B D C /\ CongH C D A B /\ CongH D C A B /\ CongH C D B A /\ CongH D C B A /\ CongH B A D C).
proof: Proof. intros. repeat split;eauto using congH_permlr, congH_perm, cong_pseudo_transitivity. 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