proposition: Lemma ncolH_exists : forall A B, A <> B -> exists C, ~ColH A B C.
proof: Proof. intros. assert (HH:= lower_dim_2). destruct HH. destruct H1. destruct H2. induction(colH_dec A B PP). induction(colH_dec A B PQ). induction(colH_dec A B PR). apply False_ind. apply H3. apply (colH_trans A B); assumption. exists PR. assumption. exists PQ. assumption. exists PP. 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