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_boxp_absorb_stable {L: Language} {minL: MinimunLanguage L} {pL: PropositionalLanguage L} {mL: ModalLanguage L} {MD: Model} {kMD: KripkeModel MD} {M: Kmodel} {R1: KM.Relation (Kworlds M)} {R2: SS.Relation (Kworlds M)} {R1_incl: Inclusion KM.Krelation SS.Krelation} {SM: Semantics L MD} {tminSM: TrivialMinimunSemantics L MD SM} {tpSM: TrivialPropositionalSemantics L MD SM} {kmSM: KripkeModalSemantics L MD M SM} {stableSM: SemanticStable L MD M SM}:
forall x: expr,
semantic_stable x ->
(forall (m: Kworlds M), KRIPKE: M, m |= x --> boxp x).