proposition: Lemma inter_incid_uniquenessH : forall P X Y l m, ~IncidL P l -> IncidL P m -> IncidL X l -> IncidL Y l -> IncidL X m -> IncidL Y m -> X = Y.
proof: Proof. intros. two_points l A B. two_points m A' B'. line_col A B X. line_col A B Y. line_col A' B' X. line_col A' B' Y. assert(~ColH A B P). intro. apply H. col_line H15 l00. lines_eq l l00. assumption. induction(eq_dec_pointsH A' P). subst P. eapply(inter_uniquenessH A B A' B'); auto. induction(eq_dec_pointsH P B'). subst P. eapply(inter_uniquenessH A B B' A'); auto. apply colH_permut_213. assumption. apply colH_permut_213. assumption. eapply(inter_uniquenessH A B P B'); auto. unfold ColH. exists m. repeat split; auto. unfold ColH. exists m. repeat split; auto. 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