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Mathlib
.
Algebra
.
Order
.
Monoid
.
Unbundled
.
OrderDual
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Imports
Init
Mathlib.Algebra.Order.Group.Synonym
Mathlib.Algebra.Order.Monoid.Unbundled.Defs
Imported by
OrderDual
.
mulLeftReflectLE
OrderDual
.
addLeftReflectLE
OrderDual
.
mulLeftMono
OrderDual
.
addLeftMono
OrderDual
.
mulRightReflectLE
OrderDual
.
addRightReflectLE
OrderDual
.
mulRightMono
OrderDual
.
addRightMono
OrderDual
.
mulLeftReflectLT
OrderDual
.
addLeftReflectLT
OrderDual
.
mulLeftStrictMono
OrderDual
.
addLeftStrictMono
OrderDual
.
mulRightReflectLT
OrderDual
.
addRightReflectLT
OrderDual
.
mulRightStrictMono
OrderDual
.
addRightStrictMono
Unbundled ordered monoid structures on the order dual.
#
source
theorem
OrderDual
.
mulLeftReflectLE
{α :
Type
u}
[
LE
α
]
[
Mul
α
]
[c :
MulLeftReflectLE
α
]
:
MulLeftReflectLE
α
ᵒᵈ
source
theorem
OrderDual
.
addLeftReflectLE
{α :
Type
u}
[
LE
α
]
[
Add
α
]
[c :
AddLeftReflectLE
α
]
:
AddLeftReflectLE
α
ᵒᵈ
source
theorem
OrderDual
.
mulLeftMono
{α :
Type
u}
[
LE
α
]
[
Mul
α
]
[c :
MulLeftMono
α
]
:
MulLeftMono
α
ᵒᵈ
source
theorem
OrderDual
.
addLeftMono
{α :
Type
u}
[
LE
α
]
[
Add
α
]
[c :
AddLeftMono
α
]
:
AddLeftMono
α
ᵒᵈ
source
theorem
OrderDual
.
mulRightReflectLE
{α :
Type
u}
[
LE
α
]
[
Mul
α
]
[c :
MulRightReflectLE
α
]
:
MulRightReflectLE
α
ᵒᵈ
source
theorem
OrderDual
.
addRightReflectLE
{α :
Type
u}
[
LE
α
]
[
Add
α
]
[c :
AddRightReflectLE
α
]
:
AddRightReflectLE
α
ᵒᵈ
source
theorem
OrderDual
.
mulRightMono
{α :
Type
u}
[
LE
α
]
[
Mul
α
]
[c :
MulRightMono
α
]
:
MulRightMono
α
ᵒᵈ
source
theorem
OrderDual
.
addRightMono
{α :
Type
u}
[
LE
α
]
[
Add
α
]
[c :
AddRightMono
α
]
:
AddRightMono
α
ᵒᵈ
source
theorem
OrderDual
.
mulLeftReflectLT
{α :
Type
u}
[
LT
α
]
[
Mul
α
]
[c :
MulLeftReflectLT
α
]
:
MulLeftReflectLT
α
ᵒᵈ
source
theorem
OrderDual
.
addLeftReflectLT
{α :
Type
u}
[
LT
α
]
[
Add
α
]
[c :
AddLeftReflectLT
α
]
:
AddLeftReflectLT
α
ᵒᵈ
source
theorem
OrderDual
.
mulLeftStrictMono
{α :
Type
u}
[
LT
α
]
[
Mul
α
]
[c :
MulLeftStrictMono
α
]
:
MulLeftStrictMono
α
ᵒᵈ
source
theorem
OrderDual
.
addLeftStrictMono
{α :
Type
u}
[
LT
α
]
[
Add
α
]
[c :
AddLeftStrictMono
α
]
:
AddLeftStrictMono
α
ᵒᵈ
source
theorem
OrderDual
.
mulRightReflectLT
{α :
Type
u}
[
LT
α
]
[
Mul
α
]
[c :
MulRightReflectLT
α
]
:
MulRightReflectLT
α
ᵒᵈ
source
theorem
OrderDual
.
addRightReflectLT
{α :
Type
u}
[
LT
α
]
[
Add
α
]
[c :
AddRightReflectLT
α
]
:
AddRightReflectLT
α
ᵒᵈ
source
theorem
OrderDual
.
mulRightStrictMono
{α :
Type
u}
[
LT
α
]
[
Mul
α
]
[c :
MulRightStrictMono
α
]
:
MulRightStrictMono
α
ᵒᵈ
source
theorem
OrderDual
.
addRightStrictMono
{α :
Type
u}
[
LT
α
]
[
Add
α
]
[c :
AddRightStrictMono
α
]
:
AddRightStrictMono
α
ᵒᵈ