- box : F → F
- box_injective : Function.Injective LO.Box.box
Instances
@[simp]
Equations
- LO.«term□_» = Lean.ParserDescr.node `LO.term□_ 76 (Lean.ParserDescr.binary `andthen (Lean.ParserDescr.symbol "□") (Lean.ParserDescr.cat `term 76))
Instances For
Equations
- LO.Box.«term⊡_» = Lean.ParserDescr.node `LO.Box.term⊡_ 76 (Lean.ParserDescr.binary `andthen (Lean.ParserDescr.symbol "⊡") (Lean.ParserDescr.cat `term 76))
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theorem
LO.Box.Subclosed.box_closed
{F : Type u_1}
[LO.Box F]
{C : F → Prop}
[self : LO.Box.Subclosed C]
{p : F}
:
C (□p) → C p
@[simp]
theorem
LO.Box.multibox_injective
{F : Type u_1}
[LO.Box F]
{n : ℕ}
:
Function.Injective fun (x : F) => □^[n]x
- dia : F → F
- dia_injective : Function.Injective LO.Dia.dia
Instances
@[simp]
Equations
- LO.«term◇_» = Lean.ParserDescr.node `LO.term◇_ 76 (Lean.ParserDescr.binary `andthen (Lean.ParserDescr.symbol "◇") (Lean.ParserDescr.cat `term 76))
Instances For
Equations
- LO.Dia.«term⟐_» = Lean.ParserDescr.node `LO.Dia.term⟐_ 76 (Lean.ParserDescr.binary `andthen (Lean.ParserDescr.symbol "⟐") (Lean.ParserDescr.cat `term 76))
Instances For
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- One or more equations did not get rendered due to their size.
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- dia_closed : ∀ {p : F}, C (◇p) → C p
Instances
theorem
LO.Dia.Subclosed.dia_closed
{F : Type u_1}
[LO.Dia F]
[LO.LogicalConnective F]
{C : F → Prop}
[self : LO.Dia.Subclosed C]
{p : F}
:
C (◇p) → C p
@[simp]
theorem
LO.Dia.multidia_injective
{F : Type u_1}
[LO.Dia F]
{n : ℕ}
:
Function.Injective fun (x : F) => ◇^[n]x
class
LO.BasicModalLogicalConnective
(F : Type u_1)
extends
LO.LogicalConnective
,
LO.Box
,
LO.Dia
:
Type u_1
Instances
class
LO.BasicModalLogicConnective.Subclosed
{F : Type u_1}
[LO.BasicModalLogicalConnective F]
(C : F → Prop)
extends
LO.LogicalConnective.Subclosed
,
LO.Box.Subclosed
,
LO.Dia.Subclosed
:
Instances
Instances
@[simp]
theorem
LO.ModalDeMorgan.dia
{F : Type u_1}
[LO.BasicModalLogicalConnective F]
[self : LO.ModalDeMorgan F]
(p : F)
:
@[simp]
theorem
LO.ModalDeMorgan.box
{F : Type u_1}
[LO.BasicModalLogicalConnective F]
[self : LO.ModalDeMorgan F]
(p : F)
:
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Instances For
Equations
- «term□''_» = Lean.ParserDescr.node `term□''_ 80 (Lean.ParserDescr.binary `andthen (Lean.ParserDescr.symbol "□''") (Lean.ParserDescr.cat `term 80))
Instances For
Equations
- «term◇''_» = Lean.ParserDescr.node `term◇''_ 80 (Lean.ParserDescr.binary `andthen (Lean.ParserDescr.symbol "◇''") (Lean.ParserDescr.cat `term 80))
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Equations
- «term□''⁻¹_» = Lean.ParserDescr.node `term□''⁻¹_ 80 (Lean.ParserDescr.binary `andthen (Lean.ParserDescr.symbol "□''⁻¹") (Lean.ParserDescr.cat `term 80))
Instances For
Equations
- «term◇''⁻¹_» = Lean.ParserDescr.node `term◇''⁻¹_ 80 (Lean.ParserDescr.binary `andthen (Lean.ParserDescr.symbol "◇''⁻¹") (Lean.ParserDescr.cat `term 80))
Instances For
@[simp]
theorem
Finset.eq_box_multibox_one
{F : Type u_1}
[DecidableEq F]
[LO.Box F]
{s : Finset F}
:
s.box = Finset.multibox 1 s
@[simp]
theorem
Finset.eq_dia_multidia_one
{F : Type u_1}
[DecidableEq F]
[LO.Dia F]
{s : Finset F}
:
s.dia = Finset.multidia 1 s
@[simp]
theorem
Finset.eq_prebox_premultibox_one
{F : Type u_1}
[LO.Box F]
{s : Finset F}
:
s.prebox = Finset.premultibox 1 s
@[simp]
theorem
Finset.eq_predia_premultidia_one
{F : Type u_1}
[LO.Dia F]
{s : Finset F}
:
s.predia = Finset.premultidia 1 s
theorem
Finset.multibox_coe
{F : Type u_1}
[DecidableEq F]
[LO.Box F]
{s : Finset F}
{n : ℕ}
:
↑(Finset.multibox n s) = □''^[n]↑s
theorem
Finset.multidia_coe
{F : Type u_1}
[DecidableEq F]
[LO.Dia F]
{s : Finset F}
{n : ℕ}
:
↑(Finset.multidia n s) = ◇''^[n]↑s
theorem
Finset.multibox_mem_coe
{F : Type u_1}
[DecidableEq F]
[LO.Box F]
{s : Finset F}
{n : ℕ}
{p : F}
:
theorem
Finset.multidia_mem_coe
{F : Type u_1}
[DecidableEq F]
[LO.Dia F]
{s : Finset F}
{n : ℕ}
{p : F}
:
theorem
Finset.premultibox_coe
{F : Type u_1}
[LO.Box F]
{s : Finset F}
{n : ℕ}
:
↑(Finset.premultibox n s) = □''⁻¹^[n]↑s
theorem
Finset.premultidia_coe
{F : Type u_1}
[LO.Dia F]
{s : Finset F}
{n : ℕ}
:
↑(Finset.premultidia n s) = ◇''⁻¹^[n]↑s
theorem
Finset.premultibox_multibox_eq_of_subset_multibox
{F : Type u_1}
[DecidableEq F]
[LO.Box F]
{n : ℕ}
{s : Finset F}
{t : Set F}
(hs : ↑s ⊆ □''^[n]t)
:
Finset.multibox n (Finset.premultibox n s) = s
theorem
Finset.prebox_box_eq_of_subset_box
{F : Type u_1}
[DecidableEq F]
[LO.Box F]
{s : Finset F}
{t : Set F}
(hs : ↑s ⊆ □''t)
:
s.prebox.box = s
theorem
Finset.premultidia_multidia_eq_of_subset_multidia
{F : Type u_1}
[DecidableEq F]
[LO.Dia F]
{n : ℕ}
{s : Finset F}
{t : Set F}
(hs : ↑s ⊆ ◇''^[n]t)
:
Finset.multidia n (Finset.premultidia n s) = s
theorem
Finset.predia_dia_eq_of_subset_dia
{F : Type u_1}
[DecidableEq F]
[LO.Dia F]
{s : Finset F}
{t : Set F}
(hs : ↑s ⊆ ◇''t)
:
s.predia.dia = s
@[reducible, inline]
Equations
- □'^[n]l = (Finset.multibox n l.toFinset).toList
Instances For
Equations
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@[reducible, inline]
Equations
- ◇'^[n]l = (Finset.multidia n l.toFinset).toList
Instances For
Equations
- One or more equations did not get rendered due to their size.
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Equations
- «term□'_» = Lean.ParserDescr.node `term□'_ 80 (Lean.ParserDescr.binary `andthen (Lean.ParserDescr.symbol "□'") (Lean.ParserDescr.cat `term 80))
Instances For
Equations
- «term◇'_» = Lean.ParserDescr.node `term◇'_ 80 (Lean.ParserDescr.binary `andthen (Lean.ParserDescr.symbol "◇'") (Lean.ParserDescr.cat `term 80))
Instances For
@[reducible, inline]
Equations
- □'⁻¹^[n]l = (Finset.premultibox n l.toFinset).toList
Instances For
Equations
- One or more equations did not get rendered due to their size.
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@[reducible, inline]
Equations
- ◇'⁻¹^[n]l = (Finset.premultidia n l.toFinset).toList
Instances For
Equations
- One or more equations did not get rendered due to their size.
Instances For
Equations
- «term□'⁻¹_» = Lean.ParserDescr.node `term□'⁻¹_ 80 (Lean.ParserDescr.binary `andthen (Lean.ParserDescr.symbol "□'⁻¹") (Lean.ParserDescr.cat `term 80))
Instances For
Equations
- «term◇'⁻¹_» = Lean.ParserDescr.node `term◇'⁻¹_ 80 (Lean.ParserDescr.binary `andthen (Lean.ParserDescr.symbol "◇'⁻¹") (Lean.ParserDescr.cat `term 80))
Instances For
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