proposition: Lemma markov_betE a b c : ~ ~ [ /\ [ \/ a 0 0 != b 0 0 | a 0 1 != b 0 1 ] & [ \/ b 0 0 != c 0 0 | b 0 1 != c 0 1 ] ] -> [ /\ [ \/ a 0 0 != b 0 0 | a 0 1 != b 0 1 ] & [ \/ b 0 0 != c 0 0 | b 0 1 != c 0 1 ] ].
proof: Proof. case: (a 0 0 =P b 0 0); case: (a 0 1 =P b 0 1); case: (b 0 0 =P c 0 0); case: (b 0 1 =P c 0 1)=> _ _ _ _ /= ?; apply Decidable.not_not=> //; apply Decidable.dec_and; apply Decidable.dec_or; solve[left=> //|right=> //]. Qed.
imports: mathcomp.ssreflect.ssreflect mathcomp(ssrbool ssrfun ssrnat eqtype seq order) mathcomp(fintype bigop) mathcomp(ssralg ssrnum matrix) mathcomp(zmodp) GeoCoq.Axioms.tarski_axioms GeoCoq.Axioms.gupta_inspired_variant_axioms GeoCoq.Meta_theory.Models.gupta_inspired_to_tarski GeoCoq.Meta_theory.Counter_models.coplanarity GeoCoq.Meta_theory.Parallel_postulates.parallel_postulates GeoCoq.Tarski_dev.Ch12_parallel_inter_dec