Require Logic.PropositionalLogic.DeepEmbedded.PropositionalLanguage.
Require Logic.PropositionalLogic.DeepEmbedded.ProofTheories.
Require Logic.PropositionalLogic.DeepEmbedded.TrivialSemantics.
Local Open Scope logic_base.
Local Open Scope syntax.
Local Open Scope kripke_model.
Local Open Scope kripke_model_class.
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.G ProofTheories.ClassicalPropositionalLogic.AX ProofTheories.ClassicalPropositionalLogic.minAX ProofTheories.ClassicalPropositionalLogic.ipG  ProofTheories.ClassicalPropositionalLogic.cpG.
Existing Instances Axiomatization2SequentCalculus_SC Axiomatization2SequentCalculus_bSC Axiomatization2SequentCalculus_fwSC Axiomatization2SequentCalculus_minSC Axiomatization2SequentCalculus_ipSC Axiomatization2SequentCalculus_cpSC.
Definition cP: context -> Prop := maximal consistent.

Lemma AL_MC: at_least (maximal consistent) cP.
Definition canonical_frame: Type := sig cP.