Documentation

Foundation.Modal.Kripke.Logic.Grz.Completeness

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noncomputable abbrev LO.Modal.Formula.subformulasGrz {α : Type u} [DecidableEq α] (φ : Formula α) :
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        theorem LO.Modal.Grz.Kripke.truthlemma_lemma2 {S : Type u_1} [Entailment (Formula ) S] {𝓢 : S} [Entailment.Grz 𝓢] {φ ψ : Formula } {X : ComplementClosedConsistentFinset 𝓢 φ.subformulasGrz} (hψ₁ : ψ φ.subformulas) (hψ₂ : ψX) :
        theorem LO.Modal.Grz.Kripke.truthlemma_lemma3 {S : Type u_1} [Entailment (Formula ) S] {𝓢 : S} [Entailment.Grz 𝓢] {φ : Formula } :
        𝓢 ⊢! φ (φ φ) φ
        theorem LO.Modal.Grz.Kripke.truthlemma {S : Type u_1} [Entailment (Formula ) S] {𝓢 : S} [Entailment.Consistent 𝓢] [Entailment.Grz 𝓢] {φ ψ : Formula } {X : (miniCanonicalModel 𝓢 φ).World} (q_sub : ψ φ.subformulas) :