@[reducible, inline]
Equations
- LO.Modal.Kripke.Frame.RelReflTransGen = Relation.ReflTransGen fun (x1 x2 : F.World) => x1 ≺ x2
Equations
- One or more equations did not get rendered due to their size.
@[simp]
theorem
LO.Modal.Kripke.Frame.RelReflTransGen.single
{F : Frame}
{x y : F.World}
(hxy : x ≺ y)
:
x ≺^* y
@[simp]
@[simp]
@[simp]
theorem
LO.Modal.Kripke.Frame.RelReflTransGen.symmetric
{F : Frame}
:
Symmetric F.Rel → Symmetric RelReflTransGen
@[reducible, inline]
Equations
- F^* = LO.Modal.Kripke.Frame.mk F.World fun (x1 x2 : F.World) => x1 ≺^* x2
Equations
- LO.Modal.Kripke.«term_^*» = Lean.ParserDescr.trailingNode `LO.Modal.Kripke.«term_^*» 95 95 (Lean.ParserDescr.symbol "^*")
theorem
LO.Modal.Kripke.Frame.TransitiveReflexiveClosure.single
{F : Frame}
{x y : F.World}
(hxy : x ≺ y)
:
F^*.Rel x y
theorem
LO.Modal.Kripke.Frame.TransitiveReflexiveClosure.rel_transitive
{F : Frame}
:
Transitive F^*.Rel
@[reducible, inline]
Equations
- LO.Modal.Kripke.Frame.RelTransGen = Relation.TransGen fun (x1 x2 : F.World) => x1 ≺ x2
Equations
- One or more equations did not get rendered due to their size.
@[simp]
@[simp]
@[simp]
@[reducible, inline]
Equations
- F^+ = LO.Modal.Kripke.Frame.mk F.World fun (x1 x2 : F.World) => x1 ≺^+ x2
Equations
- LO.Modal.Kripke.«term_^+» = Lean.ParserDescr.trailingNode `LO.Modal.Kripke.«term_^+» 95 95 (Lean.ParserDescr.symbol "^+")
theorem
LO.Modal.Kripke.Frame.TransitiveClosure.single
{F : Frame}
{x y : F.World}
(hxy : x ≺ y)
:
F^+.Rel x y
@[reducible, inline]
Equations
- LO.Modal.Kripke.Frame.RelReflGen = Relation.ReflGen fun (x1 x2 : F.World) => x1 ≺ x2
Equations
- One or more equations did not get rendered due to their size.
@[reducible, inline]
Equations
- F^= = LO.Modal.Kripke.Frame.mk F.World fun (x1 x2 : F.World) => LO.Modal.Kripke.Frame.RelReflGen x1 x2
Equations
- LO.Modal.Kripke.«term_^=» = Lean.ParserDescr.trailingNode `LO.Modal.Kripke.«term_^=» 95 95 (Lean.ParserDescr.symbol "^=")
@[reducible, inline]
Equations
- LO.Modal.Kripke.Frame.RelIrreflGen = Relation.IrreflGen fun (x1 x2 : F.World) => x1 ≺ x2
Equations
- One or more equations did not get rendered due to their size.
@[simp]
@[reducible, inline]
Equations
- F^≠ = LO.Modal.Kripke.Frame.mk F.World fun (x1 x2 : F.World) => LO.Modal.Kripke.Frame.RelIrreflGen x1 x2
Equations
- LO.Modal.Kripke.«term_^≠» = Lean.ParserDescr.trailingNode `LO.Modal.Kripke.«term_^≠» 95 95 (Lean.ParserDescr.symbol "^≠")
@[simp]