proposition: Lemma lower_dim_e : exists A, exists B, exists C, ~ (Bet A B C \/ Bet B C A \/ Bet C A B).
proof: Proof. assert(HH:=lower_dim_2). spliter. exists PP. exists PQ. exists PR. intro. apply H2. induction H3; unfold Bet in H3; induction H3. apply between_col in H3. tauto. induction H3; rewrite H3; Col. induction H3. apply between_col in H3; spliter; Col. induction H3; rewrite H3; Col. induction H3. apply between_col in H3; spliter; Col. induction H3; rewrite H3; Col. 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