proposition: Lemma axAUf s t : prv (s ---> fAX (fAU s t) ---> fAU s t).
proof: Proof. apply: rAIL. rule ax_contra. rewrite -> axAUcmp, modular_hilbert.axDN. rewrite -> axERf at 1. rule axAcase. Intro. set u := ~~: (s :/\: _). ApplyH (axOE (~~: s) (fEX (fER (~~: s) (~~: t))) u); rewrite /u. - Intro. ApplyH axAcase. do 2 Intro. Apply* 2. - Intro. ApplyH axAcase. do 2 Intro. Apply* 2. Qed.
imports: mathcomp.ssreflect.ssreflect mathcomp(all_ssreflect) CompDecModal.libs(edone bcase fset base modular_hilbert) CompDecModal.CTL(CTL_def hilbert hilbert_hist)