Local Open Scope logic_base.
Local Open Scope syntax.
Local Open Scope kripke_model.
Section Sound_Kripke.
Context {L: Language}
{minL: MinimunLanguage L}
{MD: Model}
{kMD: KripkeModel MD}
{M: Kmodel}
{R: Relation (Kworlds M)}
{po_R: PreOrder Krelation}
{SM: Semantics L MD}
{kiSM: KripkeIntuitionisticSemantics L MD M SM}
{kminSM: KripkeMinimunSemantics L MD M SM}.

(* Specifications: *)
Lemma sound_modus_ponens:
forall x y: expr,
forall m,
KRIPKE: M, m |= (x --> y) -> KRIPKE: M, m |= x -> KRIPKE: M, m |= y.
Lemma sound_axiom1:
forall x y: expr,
forall m,
KRIPKE: M, m |= x --> y --> x.
Lemma sound_axiom2:
forall x y z: expr,
forall m,
KRIPKE: M, m |= (x --> y --> z) --> (x --> y) --> (x --> z).