proposition: Lemma lower_dim_l : ~ (Bet PP PQ PR \/ Bet PQ PR PP \/ Bet PR PP PQ).
proof: Proof. intro. apply lower_dim_2. induction H; unfold Bet in H; induction H. apply between_col in H; Col. induction H; rewrite H; Col. induction H. apply between_col in H; Col. induction H; rewrite H; Col. induction H. apply between_col in H; Col. induction H; rewrite H; 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