Maximality of 𝐓𝐫𝐢𝐯
and 𝐕𝐞𝐫
#
𝐓𝐫𝐢𝐯
and 𝐕𝐞𝐫
are maximal in normal modal Foundation.
Equations
- LO.IntProp.«term_ᴹ» = Lean.ParserDescr.trailingNode `LO.IntProp.term_ᴹ 75 75 (Lean.ParserDescr.symbol "ᴹ")
Instances For
def
LO.Modal.Formula.toPropFormula
{α : Type u_1}
(p : LO.Modal.Formula α)
:
autoParam (p.degree = 0) _auto✝ → LO.IntProp.Formula α
Equations
Instances For
Equations
- LO.Modal.Formula.«term_ᴾ» = Lean.ParserDescr.trailingNode `LO.Modal.Formula.term_ᴾ 75 75 (Lean.ParserDescr.symbol "ᴾ")
Instances For
Equations
Instances For
Equations
- LO.Modal.Formula.«term_ᵀ» = Lean.ParserDescr.trailingNode `LO.Modal.Formula.term_ᵀ 75 75 (Lean.ParserDescr.symbol "ᵀ")
Instances For
@[simp]
theorem
LO.Modal.Formula.TrivTranslation.degree_zero :
∀ {α : Type u_1} {p : LO.Modal.Formula α}, pᵀ.degree = 0
@[simp]
Equations
Instances For
Equations
- LO.Modal.Formula.«term_ⱽ» = Lean.ParserDescr.trailingNode `LO.Modal.Formula.term_ⱽ 75 75 (Lean.ParserDescr.symbol "ⱽ")
Instances For
@[simp]
theorem
LO.Modal.Formula.VerTranslation.degree_zero :
∀ {α : Type u_1} {p : LO.Modal.Formula α}, pⱽ.degree = 0
@[simp]
theorem
LO.Modal.deducible_iff_trivTranslation
{α : Type u_1}
[DecidableEq α]
{p : LO.Modal.Formula α}
:
theorem
LO.Modal.deducible_iff_verTranslation
{α : Type u_1}
[DecidableEq α]
{p : LO.Modal.Formula α}
:
theorem
LO.Modal.of_classical
{α : Type u_1}
[DecidableEq α]
{mΛ : LO.Modal.Hilbert α}
{p : LO.IntProp.Formula α}
:
theorem
LO.Modal.unprovable_AxiomL_K4
{α : Type u_1}
[DecidableEq α]
[Inhabited α]
:
𝐊𝟒 ⊬ LO.Axioms.L (LO.Modal.Formula.atom default)
theorem
LO.Modal.unprovable_AxiomT_GL
{α : Type u_1}
[DecidableEq α]
[Inhabited α]
:
𝐆𝐋 ⊬ LO.Axioms.T (LO.Modal.Formula.atom default)
instance
LO.Modal.instGLConsistencyViaUnprovableAxiomT
{α : Type u_1}
[DecidableEq α]
[Inhabited α]
:
Equations
- ⋯ = ⋯