proposition: Lemma out_outH : forall P A B, Out P A B -> outH P A B.
proof: Proof. unfold Out. unfold outH. intros. spliter. induction H1. induction (eq_dec_points A B). right; right. split; auto. left. unfold Between_H. repeat split; auto. induction (eq_dec_points A B). right; right. split; auto. right; left. unfold Between_H. repeat split; auto. Qed.
imports: Morphisms GeoCoq.Axioms.hilbert_axioms GeoCoq.Axioms.parallel_postulates GeoCoq.Meta_theory.Parallel_postulates.tarski_playfair GeoCoq.Meta_theory.Parallel_postulates.SPP_ID GeoCoq.Meta_theory.Dimension_axioms.upper_dim_3 GeoCoq.Meta_theory.Parallel_postulates.parallel_postulates GeoCoq.Utils.triples