Context {s'L: SeparationEmpLanguage L}
{EmpsGamma: EmpSeparationLogic L Gamma}
{feSM: EmpSemantics L MD M SM}.
Instance unitSA
(AL_DC: at_least derivable_closed cP)
(LIN_SR: forall (Phi: context) (Psi: sig cP), Lindenbaum_constructable (context_sepcon_included_r Phi (proj1_sig Psi)) cP)
(TRUTH: forall x, forall m Phi, rel m Phi -> (KRIPKE: M, m |= x <-> proj1_sig Phi x)):
UnitalSeparationAlgebra (Kworlds M).

Lemma nonsplit_canonical_split_smaller
{nssGamma: NonsplitEmpSeparationLogic L Gamma}
(AL_DC: at_least derivable_closed cP)
(TRUTH: forall x, forall m Phi, rel m Phi -> (KRIPKE: M, m |= x <-> proj1_sig Phi x)):
IncreasingSplitSmallerSeparationAlgebra (Kworlds M).