Section Canonical.
Context {L: Language}
{Gamma: Derivable L}
{bSC: BasicSequentCalculus L Gamma}
{MD: Model}
{kMD: KripkeModel MD}
{M: Kmodel}
{R: Relation (Kworlds M)}
{SM: Semantics L MD}.
Context (cP: context -> Prop)
(rel: bijection (Kworlds M) (sig cP)).
Hypothesis H_R: forall m n Phi Psi, rel m Phi -> rel n Psi -> (m <= n <-> Included _ (proj1_sig Phi) (proj1_sig Psi)).

Lemma denote_monotonic (x: expr):
(forall m Phi, rel m Phi -> (KRIPKE: M, m |= x <-> proj1_sig Phi x)) ->
upwards_closed_Kdenote (Kdenotation M x).