Documentation

Foundation.Modal.Kripke.NNFormula

@[simp]
theorem LO.Modal.NNFormula.Kripke.Satisfies.atom_def {M : Kripke.Model} {x : M.World} (a : ) :
x atom a M.Val x a
@[simp]
theorem LO.Modal.NNFormula.Kripke.Satisfies.natom_def {M : Kripke.Model} {x : M.World} (a : ) :
x natom a ¬M.Val x a
theorem LO.Modal.NNFormula.Kripke.Satisfies.or_def {φ ψ : NNFormula } {M : Kripke.Model} {x : M.World} :
x φ ψ x φ x ψ
theorem LO.Modal.NNFormula.Kripke.Satisfies.and_def {φ ψ : NNFormula } {M : Kripke.Model} {x : M.World} :
x φ ψ x φ x ψ
theorem LO.Modal.NNFormula.Kripke.Satisfies.box_def {φ : NNFormula } {M : Kripke.Model} {x : M.World} :
x φ ∀ (y : M.World), x yy φ
theorem LO.Modal.NNFormula.Kripke.Satisfies.dia_def {φ : NNFormula } {M : Kripke.Model} {x : M.World} :
x φ ∃ (y : M.World), x y y φ
theorem LO.Modal.NNFormula.Kripke.Satisfies.imp_def {φ ψ : NNFormula } {M : Kripke.Model} {x : M.World} :
x φ ψ x φx ψ