End Sound_Trivial.
Module Sound_KripkeIntuitionistic.

Lemma sound_stable_proper_iffp {L: Language} {minL: MinimunLanguage L} {pL: PropositionalLanguage L} {MD: Model} {kMD: KripkeModel MD} {M: Kmodel} {R1: KI.Relation (Kworlds M)} {po_R: PreOrder KI.Krelation} {R2: SS.Relation (Kworlds M)} {SM: Semantics L MD} {kiSM: KripkeIntuitionisticSemantics L MD M SM} {kminSM: KripkeMinimunSemantics L MD M SM} {kpSM: KripkePropositionalSemantics L MD M SM} {stableSM: SemanticStable L MD M SM}:
forall x y,
(forall m, KRIPKE: M, m |= x <--> y) ->
(semantic_stable x <-> semantic_stable y).