proposition: Lemma ER2 (xm : XM) P Q w : pER R P Q w -> cER R P Q w.
proof: Proof. move => H. apply: (dn xm) => C. have H' : pER R (PredC (PredC P)) (PredC (PredC Q)) w. apply: pER_strengthen H => v; by firstorder. apply pAU_pER in H'. apply: H'. apply: AU1. apply: (dn xm) => C'. apply (dmAU xm) in C'. apply: C. apply: ER_strengthen C' => ?; exact: (dn xm). Qed.
imports: mathcomp.ssreflect.ssreflect mathcomp(all_ssreflect) CompDecModal.libs(edone bcase fset base modular_hilbert) CompDecModal.CTL(CTL_def hilbert)