Local Open Scope logic_base.
Local Open Scope syntax.
Local Open Scope kripke_model.
Section TruthLemma.
Context {L: Language}
{minL: MinimunLanguage L}
{pL: PropositionalLanguage L}
{Gamma: ProofTheory L}
{bSC: BasicSequentCalculus L Gamma}
{minSC: MinimunSequentCalculus L Gamma}
{ipSC: IntuitionisticPropositionalSequentCalculus L Gamma}
{cpSC: ClassicalPropositionalSequentCalculus L Gamma}
{MD: Model}
{kMD: KripkeModel MD}
{M: Kmodel}
{SM: Semantics L MD}
{tminSM: TrivialMinimunSemantics L MD SM}
{tpSM: TrivialPropositionalSemantics L MD SM}.
Context (cP: context -> Prop)
(rel: bijection (Kworlds M) (sig cP)).
Context (AL_MC: at_least (maximal consistent) cP).

Lemma truth_lemma_falsep:
forall m Phi, rel m Phi -> (KRIPKE: M, m |= falsep <-> proj1_sig Phi falsep).