proposition: Lemma strong_pasch : forall A B C l p, ~ ColH A B C -> IncidP A p -> IncidP B p -> IncidP C p -> IncidLP l p -> ~ IncidL C l -> cut l A B -> cut l A C /\ ~ cut l B C \/ cut l B C /\ ~ cut l A C.
proof: Proof. intros. induction (pasch A B C l p); trivial. left. split; auto. apply(cut2_not_cut A B C l); auto. right. split; auto. apply(cut2_not_cut B A C l); auto. intro. apply H; Col. apply cut_comm. 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