proposition: Lemma AR_ind s t u : prv (u ---> t) -> prv (u ---> (s ---> fF) ---> fAX u) -> prv (u ---> fAR s t).
proof: Proof. move => H1 H2. apply: ARel. Intro. ApplyH axAI; [ApplyH H1|]. Intro. Have (fAX u); [by ApplyH H2|drop]. apply: rNorm. Intro. ApplyH ARI. ApplyH axOIr. ApplyH axOIl. ApplyH H1. Qed.
imports: mathcomp.ssreflect.ssreflect mathcomp(all_ssreflect) CompDecModal.libs(edone bcase fset base modular_hilbert) CompDecModal.CTL(CTL_def hilbert hilbert_hist)