proposition: Lemma out_same_side' : forall X Y A B C l , X <> Y -> IncidL X l -> IncidL Y l -> IncidL A l -> ~ IncidL B l-> outH A B C -> same_side' B C X Y.
proof: Proof. intros. assert(HH:= out_same_side A B C l H2 H3 H4). unfold same_side'. split; auto. intros. lines_eq l l0. 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