Instance SA
         (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):
  SeparationAlgebra (Kworlds M).Instance uSA
         (AL_DC: at_least derivable_closed cP):
  UpwardsClosedSeparationAlgebra (Kworlds M).Instance dSA
         (AL_DC: at_least derivable_closed cP):
  DownwardsClosedSeparationAlgebra (Kworlds M).

Lemma ext_canonical_residual {ExtSGamma: ExtSeparationLogic L Gamma} (AL_DC: at_least derivable_closed cP) (LIN_SL: forall (Phi: context) (Psi: sig cP), Lindenbaum_constructable (context_sepcon_included_l Phi (proj1_sig Psi)) cP): ResidualSeparationAlgebra (Kworlds M).