proposition: Lemma segment_constructionH : forall A B C D : Point, A <> B -> C <> D -> exists E : Point, BetH A B E /\ CongH B E C D.
proof: Proof. Proof. intros. assert(HH:= segment_construction A B C D). ex_and HH E. induction H1. induction H2. spliter. exists E. split; auto. spliter. subst E. apply betH_distincts in H1. tauto. induction H1. contradiction. subst E. induction H2. tauto. 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