proposition: Lemma inter_uniquenessH : forall A B A' B' X Y, A' <> B' -> ~ColH A B A' -> ColH A B X -> ColH A B Y -> ColH A' B' X -> ColH A' B' Y -> X = Y.
proof: Proof. intros A B A' B' X Y HD. intros. assert(A <> B). intro;subst B;apply H; Col. induction(eq_dec_pointsH X Y). assumption. apply False_ind. apply H. ColHR. 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