Section Complete.
Context {Sigma: PropositionalLanguage.PropositionalVariables}
{CV: Countable PropositionalLanguage.Var}.
Existing Instances PropositionalLanguage.L PropositionalLanguage.minL PropositionalLanguage.pL.
Existing Instances TrivialSemantics.MD TrivialSemantics.SM TrivialSemantics.tminSM TrivialSemantics.tpSM.
Existing Instances ProofTheories.ClassicalPropositionalLogic.GP ProofTheories.ClassicalPropositionalLogic.GD ProofTheories.ClassicalPropositionalLogic.AX ProofTheories.ClassicalPropositionalLogic.minAX ProofTheories.ClassicalPropositionalLogic.ipAX ProofTheories.ClassicalPropositionalLogic.cpAX.
Existing Instances Axiomatization2SequentCalculus_SC Axiomatization2SequentCalculus_bSC Axiomatization2SequentCalculus_fwSC Axiomatization2SequentCalculus_minSC Axiomatization2SequentCalculus_ipSC Axiomatization2SequentCalculus_cpSC.
Definition cP: context -> Prop := maximal consistent.
Definition canonical_frame: Type := sig cP.
Definition canonical_eval: PropositionalLanguage.Var -> canonical_frame -> Prop :=
fun p a => proj1_sig a (PropositionalLanguage.varp p).
Definition kMD: KripkeModel TrivialSemantics.MD :=
Build_KripkeModel TrivialSemantics.MD
unit (fun _ => canonical_frame) (fun u a v => canonical_eval v a).
Definition canonical_Kmodel: @Kmodel TrivialSemantics.MD kMD := tt.
Definition rel: bijection (Kworlds canonical_Kmodel) (sig cP) := bijection_refl.

Lemma TRUTH:
forall x: expr, forall m Phi, rel m Phi ->
(KRIPKE: canonical_Kmodel, m |= x <-> proj1_sig Phi x).