proposition: Lemma LPO_of_disjunctive_AR : (forall n, f n = false) \/ exists n, f n = true.
proof: Proof. Proof using hyp_AR. case: (hyp_AR AR3_0 path_pi3 (erefl _)) => H; [left|right]. - move => n. apply: contraTF (H n.+3) => Hn. rewrite /= (_ : [exists m : 'I_n.+2, f m] = true) //=. apply/existsP. have On : n < n.+2 by done. by exists (Ordinal On). - case: H => [[|n]] //=. do 2 (case: (ifP _) => //=). by exists n. Qed.
imports: mathcomp.ssreflect.ssreflect mathcomp(all_ssreflect) CompDecModal.libs(edone bcase fset base modular_hilbert) CompDecModal.CTL(CTL_def hilbert)