@[reducible, inline]
abbrev
LO.System.Axioms.Geach
{F : Type u_1}
[LO.LogicalConnective F]
[LO.BasicModalLogicalConnective F]
(l : LO.System.Axioms.Geach.Taple)
(p : F)
:
F
Instances For
@[reducible, inline]
Equations
- ๐ด๐ฒ(l) = {x : LO.Modal.Standard.Formula ฮฑ | โ (p : LO.Modal.Standard.Formula ฮฑ), LO.System.Axioms.Geach l p = x}
Instances For
Equations
- One or more equations did not get rendered due to their size.
Instances For
- taple : LO.System.Axioms.Geach.Taple
- char : Ax = ๐ด๐ฒ(LO.Modal.Standard.AxiomSet.IsGeach.taple Ax)
Instances
theorem
LO.Modal.Standard.AxiomSet.IsGeach.char
{ฮฑ : Type u_1}
{Ax : LO.Modal.Standard.AxiomSet ฮฑ}
[self : Ax.IsGeach]
:
Equations
- LO.Modal.Standard.AxiomSet.instIsGeachSetFormula = { taple := { i := 0, j := 0, m := 1, n := 0 }, char := โฏ }
Equations
- LO.Modal.Standard.AxiomSet.instIsGeachSetFormula_1 = { taple := { i := 0, j := 1, m := 0, n := 1 }, char := โฏ }
Equations
- LO.Modal.Standard.AxiomSet.instIsGeachSetFormula_2 = { taple := { i := 0, j := 0, m := 1, n := 1 }, char := โฏ }
Equations
- LO.Modal.Standard.AxiomSet.instIsGeachSetFormula_3 = { taple := { i := 0, j := 2, m := 1, n := 0 }, char := โฏ }
Equations
- LO.Modal.Standard.AxiomSet.instIsGeachSetFormula_4 = { taple := { i := 1, j := 1, m := 0, n := 1 }, char := โฏ }
Equations
- LO.Modal.Standard.AxiomSet.instIsGeachSetFormula_5 = { taple := { i := 1, j := 1, m := 1, n := 1 }, char := โฏ }
Equations
- LO.Modal.Standard.AxiomSet.instIsGeachSetFormula_6 = { taple := { i := 0, j := 1, m := 2, n := 0 }, char := โฏ }
Equations
- LO.Modal.Standard.AxiomSet.instIsGeachSetFormula_7 = { taple := { i := 1, j := 1, m := 0, n := 0 }, char := โฏ }
Equations
- LO.Modal.Standard.AxiomSet.instIsGeachSetFormula_8 = { taple := { i := 0, j := 1, m := 0, n := 0 }, char := โฏ }
Equations
- One or more equations did not get rendered due to their size.
Instances For
@[simp]
theorem
LO.Modal.Standard.AxiomSet.MultiGeach.iff_cons
{ฮฑ : Type u_1}
{x : LO.System.Axioms.Geach.Taple}
{l : List LO.System.Axioms.Geach.Taple}
:
theorem
LO.Modal.Standard.AxiomSet.MultiGeach.mem
{ฮฑ : Type u_1}
{x : LO.System.Axioms.Geach.Taple}
{l : List LO.System.Axioms.Geach.Taple}
(h : x โ l)
:
@[reducible, inline]
abbrev
LO.Modal.Standard.DeductionParameter.Geach
{ฮฑ : Type u_1}
(l : List LO.System.Axioms.Geach.Taple)
:
Instances For
Equations
- One or more equations did not get rendered due to their size.
Instances For
class
LO.Modal.Standard.DeductionParameter.IsGeach
{ฮฑ : Type u_1}
(L : LO.Modal.Standard.DeductionParameter ฮฑ)
:
- taples : List LO.System.Axioms.Geach.Taple
Instances
theorem
LO.Modal.Standard.DeductionParameter.IsGeach.char
{ฮฑ : Type u_1}
{L : LO.Modal.Standard.DeductionParameter ฮฑ}
[self : L.IsGeach]
:
theorem
LO.Modal.Standard.DeductionParameter.IsGeach.ax
{ฮฑ : Type u_1}
{ฮ : LO.Modal.Standard.DeductionParameter ฮฑ}
[geach : ฮ.IsGeach]
:
instance
LO.Modal.Standard.DeductionParameter.IsGeach.instIsNormal
{ฮฑ : Type u_1}
{L : LO.Modal.Standard.DeductionParameter ฮฑ}
[geach : L.IsGeach]
:
L.IsNormal
Equations
- LO.Modal.Standard.DeductionParameter.IsGeach.instIsNormal = โฏ.mpr inferInstance
Equations
- LO.Modal.Standard.DeductionParameter.IsGeach.instK = { taples := [], char := โฏ }
Equations
- LO.Modal.Standard.DeductionParameter.IsGeach.instKD = { taples := [{ i := 0, j := 0, m := 1, n := 1 }], char := โฏ }
Equations
- LO.Modal.Standard.DeductionParameter.IsGeach.instKT = { taples := [{ i := 0, j := 0, m := 1, n := 0 }], char := โฏ }
Equations
- LO.Modal.Standard.DeductionParameter.IsGeach.instKTB = { taples := [{ i := 0, j := 0, m := 1, n := 0 }, { i := 0, j := 1, m := 0, n := 1 }], char := โฏ }
Equations
- LO.Modal.Standard.DeductionParameter.IsGeach.instK4 = { taples := [{ i := 0, j := 2, m := 1, n := 0 }], char := โฏ }
Equations
- LO.Modal.Standard.DeductionParameter.IsGeach.instS4 = { taples := [{ i := 0, j := 0, m := 1, n := 0 }, { i := 0, j := 2, m := 1, n := 0 }], char := โฏ }
instance
LO.Modal.Standard.DeductionParameter.IsGeach.instS4Dot2
{ฮฑ : Type u_1}
:
๐๐.๐.IsGeach
Equations
- One or more equations did not get rendered due to their size.
Equations
- LO.Modal.Standard.DeductionParameter.IsGeach.instS5 = { taples := [{ i := 0, j := 0, m := 1, n := 0 }, { i := 1, j := 1, m := 0, n := 1 }], char := โฏ }
instance
LO.Modal.Standard.DeductionParameter.IsGeach.instKT4B
{ฮฑ : Type u_1}
:
๐๐๐๐.IsGeach
Equations
- One or more equations did not get rendered due to their size.
instance
LO.Modal.Standard.DeductionParameter.IsGeach.instTriv
{ฮฑ : Type u_1}
:
๐๐ซ๐ข๐ฏ.IsGeach
Equations
- LO.Modal.Standard.DeductionParameter.IsGeach.instTriv = { taples := [{ i := 0, j := 0, m := 1, n := 0 }, { i := 0, j := 1, m := 0, n := 0 }], char := โฏ }