proposition: Lemma cinterp_mono: forall i j c s, i <= j -> cinterp i c s <<= cinterp j c s.
proof: Proof. induction i as [ | i]; intros; cbn. - auto with lessdef. - destruct j as [ | j]. lia. cbn. destruct c; auto with lessdef. + apply bind_mono. apply IHi; lia. intros; apply IHi; lia. + apply IHi; lia. + destruct (beval b s); auto with lessdef. apply bind_mono. apply IHi; lia. intros; apply IHi; lia. Qed.
imports: Coq(Arith ZArith Psatz Bool String List) CDF(Sequences IMP Compil) Coq(Classical Description)