Section BILogicMorphisms.
Context {A : BILogicType} `{BIL: BILogic A}.
Global Instance sepSP_lentails_m:
Proper (lentails ++> lentails ++> lentails) sepSP.
Global Instance sepSP_lequiv_m:
Proper (lequiv ==> lequiv ==> lequiv) sepSP.
Global Instance wandSP_lentails_m:
Proper (lentails --> lentails ++> lentails) wandSP.
Global Instance wandSP_lequiv_m:
Proper (lequiv ==> lequiv ==> lequiv) wandSP.
End BILogicMorphisms.
Section DerivedInferenceRules.
Context {A : BILogicType} `{BILogic A}.

Lemma siexistsE {T : Type} (P : T -> A) (Q : A) :
lexists P -* Q -|- Forall x, (P x -* Q).