proposition: Lemma congH_perm : forall A B, A<>B -> CongH A B B A.
proof: Proof. intros. destruct (line_existence A B H) as [l []]. elim (cong_existence A B A B l); auto; intros B' H2. spliter. apply cong_pseudo_transitivity with A B'. assumption. apply cong_permr. 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