proposition: Lemma axARu s t : prv (fAR s t ---> (s ---> fF) ---> fAX (fAR s t)).
proof: Proof. rewrite -> axARdef at 1. rewrite -> axEUeq,dmO,dmA. set u := fEU _ _. rewrite -[~~: fEX u]/(~~: (~~: (fAX (~~: u)))). do ! rewrite -> axDNE. rewrite /u. rewrite <- axARdef. rule axAcase. Intro. ApplyH axOE. ApplyH axContra. do 2 Intro. by Asm. Qed.
imports: mathcomp.ssreflect.ssreflect mathcomp(all_ssreflect) CompDecModal.libs(edone bcase fset base modular_hilbert) CompDecModal.CTL(CTL_def hilbert)