Require Logic.PropositionalLogic.Semantics.Trivial.
Require Logic.ModalLogic.Semantics.Kripke.
Require Logic.GeneralLogic.Semantics.Kripke.
Require Logic.MinimunLogic.Semantics.Kripke.
Require Logic.PropositionalLogic.Semantics.Kripke.
Require Logic.ModalLogic.Semantics.Flat.
Require Logic.SeparationLogic.Semantics.FlatSemantics.
Local Open Scope logic_base.
Local Open Scope syntax.
Local Open Scope kripke_model.
Module Sound_Trivial.

Lemma sound_stable_proper_iffp {L: Language} {minL: MinimunLanguage L} {pL: PropositionalLanguage L} {MD: Model} {kMD: KripkeModel MD} {M: Kmodel} {R: SS.Relation (Kworlds M)} {SM: Semantics L MD} {tminSM: TrivialMinimunSemantics L MD SM} {tpSM: TrivialPropositionalSemantics L MD SM} {stableSM: SemanticStable L MD M SM}:
forall x y,
(forall m, KRIPKE: M, m |= x <--> y) ->
(semantic_stable x <-> semantic_stable y).