Section Complete.
Context (Var: Type) (CV: Countable Var).
Instance L: Language := MinimumLanguage.L Var.
Instance minL: MinimumLanguage L := MinimumLanguage.minL Var.
Instance GP: Provable L := MinimumLogic.GP Var.
Instance GD: Derivable L := MinimumLogic.GD Var.
Instance AX: NormalAxiomatization L GP GD := MinimumLogic.AX Var.
Instance minAX: MinimumAxiomatization L GP := MinimumLogic.minAX Var.
Instance SC: NormalSequentCalculus L GP GD := MinimumLogic.SC Var.
Instance bSC: BasicSequentCalculus L GD := MinimumLogic.bSC Var.
Instance fwSC: FiniteWitnessedSequentCalculus L GD := MinimumLogic.fwSC Var.
Instance minSC: MinimumSequentCalculus L GD := MinimumLogic.minSC 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_kminSM (M: Kmodel): KripkeMinimumSemantics L Kripke_MD M Kripke_SM := KripkeSemantics.kminSM Var M.
Definition cP: context -> Prop := derivable_closed.
Definition canonical_frame: KripkeSemantics.frame :=
KripkeSemantics.Build_frame (sig cP) (fun a b => Included _ (proj1_sig a) (proj1_sig b)).
Definition canonical_eval: Var -> KripkeSemantics.sem canonical_frame :=
fun p a => proj1_sig a (MinimumLanguage.varp p).
Definition canonical_Kmodel: @Kmodel (KripkeSemantics.MD Var) (KripkeSemantics.kMD Var) :=
KripkeSemantics.Build_Kmodel Var canonical_frame canonical_eval.
Definition rel: bijection (Kworlds canonical_Kmodel) (sig cP) := bijection_refl.
Definition H_R:
forall m n Phi Psi, rel m Phi -> rel n Psi ->
(m <= n <-> Included _ (proj1_sig Phi) (proj1_sig Psi)).

Theorem complete_MinimumLogic_Kripke_all:
strongly_complete GD Kripke_SM
(KripkeModelClass _ (Kmodel_Monotonic + Kmodel_PreOrder)).