Documentation
APAP
.
Mathlib
.
Algebra
.
Group
.
Pointwise
.
Set
.
Basic
Search
return to top
source
Imports
Init
AddCombi.Mathlib.Algebra.Notation.Indicator
Mathlib.Algebra.Group.Pointwise.Set.Basic
Imported by
indicator_one_inv
indicator_one_neg
source
@[simp]
theorem
indicator_one_inv
{
G
:
Type
u_1}
{
M₀
:
Type
u_2}
[
One
M₀
]
[
Zero
M₀
]
[
Group
G
]
(
s
:
Set
G
)
(
a
:
G
)
:
s
⁻¹
.
indicator
(fun (
x
:
G
) =>
1
)
a
=
s
.
indicator
(fun (
x
:
G
) =>
1
)
a
⁻¹
source
@[simp]
theorem
indicator_one_neg
{
G
:
Type
u_1}
{
M₀
:
Type
u_2}
[
One
M₀
]
[
Zero
M₀
]
[
AddGroup
G
]
(
s
:
Set
G
)
(
a
:
G
)
:
(
-
s
).
indicator
(fun (
x
:
G
) =>
1
)
a
=
s
.
indicator
(fun (
x
:
G
) =>
1
)
(
-
a
)