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.

Lemma AL_MC: at_least (maximal consistent) cP.