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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
instance
OrderDual
.
mulLeftReflectLE
{
α
:
Type
u}
[
LE
α
]
[
Mul
α
]
[
c
:
MulLeftReflectLE
α
]
:
MulLeftReflectLE
α
ᵒᵈ
source
instance
OrderDual
.
addLeftReflectLE
{
α
:
Type
u}
[
LE
α
]
[
Add
α
]
[
c
:
AddLeftReflectLE
α
]
:
AddLeftReflectLE
α
ᵒᵈ
source
instance
OrderDual
.
mulLeftMono
{
α
:
Type
u}
[
LE
α
]
[
Mul
α
]
[
c
:
MulLeftMono
α
]
:
MulLeftMono
α
ᵒᵈ
source
instance
OrderDual
.
addLeftMono
{
α
:
Type
u}
[
LE
α
]
[
Add
α
]
[
c
:
AddLeftMono
α
]
:
AddLeftMono
α
ᵒᵈ
source
instance
OrderDual
.
mulRightReflectLE
{
α
:
Type
u}
[
LE
α
]
[
Mul
α
]
[
c
:
MulRightReflectLE
α
]
:
MulRightReflectLE
α
ᵒᵈ
source
instance
OrderDual
.
addRightReflectLE
{
α
:
Type
u}
[
LE
α
]
[
Add
α
]
[
c
:
AddRightReflectLE
α
]
:
AddRightReflectLE
α
ᵒᵈ
source
instance
OrderDual
.
mulRightMono
{
α
:
Type
u}
[
LE
α
]
[
Mul
α
]
[
c
:
MulRightMono
α
]
:
MulRightMono
α
ᵒᵈ
source
instance
OrderDual
.
addRightMono
{
α
:
Type
u}
[
LE
α
]
[
Add
α
]
[
c
:
AddRightMono
α
]
:
AddRightMono
α
ᵒᵈ
source
instance
OrderDual
.
mulLeftReflectLT
{
α
:
Type
u}
[
LT
α
]
[
Mul
α
]
[
c
:
MulLeftReflectLT
α
]
:
MulLeftReflectLT
α
ᵒᵈ
source
instance
OrderDual
.
addLeftReflectLT
{
α
:
Type
u}
[
LT
α
]
[
Add
α
]
[
c
:
AddLeftReflectLT
α
]
:
AddLeftReflectLT
α
ᵒᵈ
source
instance
OrderDual
.
mulLeftStrictMono
{
α
:
Type
u}
[
LT
α
]
[
Mul
α
]
[
c
:
MulLeftStrictMono
α
]
:
MulLeftStrictMono
α
ᵒᵈ
source
instance
OrderDual
.
addLeftStrictMono
{
α
:
Type
u}
[
LT
α
]
[
Add
α
]
[
c
:
AddLeftStrictMono
α
]
:
AddLeftStrictMono
α
ᵒᵈ
source
instance
OrderDual
.
mulRightReflectLT
{
α
:
Type
u}
[
LT
α
]
[
Mul
α
]
[
c
:
MulRightReflectLT
α
]
:
MulRightReflectLT
α
ᵒᵈ
source
instance
OrderDual
.
addRightReflectLT
{
α
:
Type
u}
[
LT
α
]
[
Add
α
]
[
c
:
AddRightReflectLT
α
]
:
AddRightReflectLT
α
ᵒᵈ
source
instance
OrderDual
.
mulRightStrictMono
{
α
:
Type
u}
[
LT
α
]
[
Mul
α
]
[
c
:
MulRightStrictMono
α
]
:
MulRightStrictMono
α
ᵒᵈ
source
instance
OrderDual
.
addRightStrictMono
{
α
:
Type
u}
[
LT
α
]
[
Add
α
]
[
c
:
AddRightStrictMono
α
]
:
AddRightStrictMono
α
ᵒᵈ