proposition: Lemma dmAU (xm : XM) w : ~ cAU R P Q w -> cER R (PredC P) (PredC Q) w.
proof: Proof. move: w. cofix dmAU => w Hw. have nQw: (~ Q w). move => c. apply Hw. exact: AU0. case: (xm (P w)) => [pw|nPw]; last exact: ER0. suff {dmAU} [v v1 v2] : exists2 v, R w v & ~ cAU R P Q v. apply: ERs v1 _. exact: nQw. exact: dmAU. apply: (dn xm) => C. apply: Hw. apply: AUs pw _ => v wv. apply: (dn xm) => C'. apply: C. by exists v. Qed.
imports: mathcomp.ssreflect.ssreflect mathcomp(all_ssreflect) CompDecModal.libs(edone bcase fset base modular_hilbert) CompDecModal.CTL(CTL_def hilbert)