@[reducible, inline]
Equations
- LO.Kripke.IrreflexiveFrameClass = {F : LO.Kripke.Frame | Irreflexive F.Rel}
Instances For
def
LO.Modal.Kripke.ModalEquivalent
{α : Type u_1}
{M₁ : LO.Kripke.Model α}
{M₂ : LO.Kripke.Model α}
(w₁ : M₁.World)
(w₂ : M₂.World)
:
Instances For
Equations
- LO.Modal.Kripke.«term_↭_» = Lean.ParserDescr.trailingNode `LO.Modal.Kripke.term_↭_ 50 51 (Lean.ParserDescr.binary `andthen (Lean.ParserDescr.symbol " ↭ ") (Lean.ParserDescr.cat `term 51))
Instances For
theorem
LO.Modal.Kripke.modal_equivalent_of_bisimilar
{α : Type u_1}
{M₁ : LO.Kripke.Model α}
{M₂ : LO.Kripke.Model α}
{x₁ : M₁.World}
{x₂ : M₂.World}
(Bi : M₁ ⇄ M₂)
(bisx : Bi.toRel x₁ x₂)
:
x₁ ↭ x₂
theorem
LO.Modal.Kripke.modal_equivalence_of_modal_morphism
{α : Type u_1}
{M₁ : LO.Kripke.Model α}
{M₂ : LO.Kripke.Model α}
(f : M₁ →ₚ M₂)
(w : M₁.World)
:
w ↭ f.toFun w
theorem
LO.Modal.Kripke.iff_formula_valid_on_frame_surjective_morphism
{α : Type u_1}
{F₁ : LO.Kripke.Frame}
{F₂ : LO.Kripke.Frame}
{p : LO.Modal.Formula α}
(f : F₁ →ₚ F₂)
(f_surjective : Function.Surjective f.toFun)
:
theorem
LO.Modal.Kripke.iff_theory_valid_on_frame_surjective_morphism
{α : Type u_1}
{F₁ : LO.Kripke.Frame}
{F₂ : LO.Kripke.Frame}
{T : Set (LO.Modal.Formula α)}
(f : F₁ →ₚ F₂)
(f_surjective : Function.Surjective f.toFun)
:
theorem
LO.Modal.Kripke.undefinable_irreflexive
{α : Type u_1}
:
¬∃ (Λ : LO.Modal.Hilbert α), ∀ (F : LO.Kripke.Frame), F ∈ 𝔽(Λ) ↔ F ∈ LO.Kripke.IrreflexiveFrameClass
theorem
LO.Modal.Kripke.modal_equivalent_at_root_on_generated_model
{α : Type u_1}
(M : LO.Kripke.Model α)
(M_trans : Transitive M.Frame.Rel)
(r : M.World)
:
⟨r, ⋯⟩ ↭ r