proposition: Lemma AU_ind s t u : prv (t ---> u) -> prv (s ---> fAX u ---> u) -> prv ((fAU s t) ---> u).
proof: Proof. move => H1 H2. rewrite -> (axA2 (fAU s t)). rule axAcase. apply: AU_ind_aux. - rewrite <- H1. exact: axK. - rewrite -> axAUeq at 2. Intro. ApplyH axOE; first by ApplyH H1. ApplyH axAcase. do 2 Intro. ApplyH H2. ApplyH (axN (fAU s t)). Qed.
imports: mathcomp.ssreflect.ssreflect mathcomp(all_ssreflect) CompDecModal.libs(edone bcase fset base modular_hilbert) CompDecModal.CTL(CTL_def hilbert)