proposition: Lemma not_cut3 : forall A B C l p, IncidP A p -> IncidP B p -> IncidP C p -> IncidLP l p -> ~ IncidL A l -> ~ ColH A B C -> ~ cut l A B -> ~ cut l A C -> ~ cut l B C.
proof: Proof. intros. intro. assert(~ColH B C A). intro. apply H4; Col. assert(HH:= pasch B C A l p). induction HH; trivial. apply cut_comm in H9. contradiction. apply cut_comm in H9. contradiction. 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