Require Logic.MinimunLogic.Sound.Sound_Classical_Trivial.
Require Logic.MinimunLogic.Sound.Sound_Kripke.
Require Logic.PropositionalLogic.Sound.Sound_Classical_Trivial.
Require Logic.PropositionalLogic.Sound.Sound_Kripke.
Require Logic.PropositionalLogic.DeepEmbedded.PropositionalLanguage.
Require Logic.PropositionalLogic.DeepEmbedded.ProofTheories.
Require Logic.PropositionalLogic.DeepEmbedded.TrivialSemantics.
Require Logic.PropositionalLogic.DeepEmbedded.KripkeSemantics.
Local Open Scope logic_base.
Local Open Scope syntax.
Local Open Scope kripke_model.
Local Open Scope kripke_model_class.
Section Sound.
Context {Sigma: PropositionalLanguage.PropositionalVariables}.
Existing Instances PropositionalLanguage.L PropositionalLanguage.minL PropositionalLanguage.pL.
(* Instance Intuitionistic_G: ProofTheory L := IntuitionisticLogic.G Var. Instance DeMorgan_G: ProofTheory L := DeMorganLogic.G Var. Instance GodelDummett_G: ProofTheory L := GodelDummettLogic.G Var. Instance Classical_G: ProofTheory L := ClassicalLogic.G Var. Instance Trivial_MD: Model := TrivialSemantics.MD Var. Instance Trivial_SM: Semantics L Trivial_MD := TrivialSemantics.SM Var. Instance Kripke_MD: Model := KripkeSemantics.MD Var. Instance Kripke_kMD: KripkeModel Kripke_MD := KripkeSemantics.kMD Var. Instance Kripke_R (M: Kmodel): Relation (Kworlds M) := KripkeSemantics.R Var M. Instance Kripke_SM: Semantics L Kripke_MD := KripkeSemantics.SM Var. Instance Kripke_kpSM (M: Kmodel): KripkePropositionalSemantics L Kripke_MD M Kripke_SM := KripkeSemantics.kpSM Var M. *)
Section Sound_Classical_Trivial.
Existing Instances ProofTheories.ClassicalPropositionalLogic.minAX ProofTheories.ClassicalPropositionalLogic.ipG.
Existing Instances TrivialSemantics.MD TrivialSemantics.SM TrivialSemantics.tminSM TrivialSemantics.tpSM.

Theorem sound_classical_trivial: sound ProofTheories.ClassicalPropositionalLogic.G TrivialSemantics.SM (AllModel _).
End Sound_Classical_Trivial.