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Mathlib
.
Algebra
.
GroupWithZero
.
Conj
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Imports
Init
Mathlib.Algebra.Group.Conj
Mathlib.Algebra.GroupWithZero.Units.Basic
Imported by
GroupWithZero
.
isConj_iff₀
GroupWithZero
.
conj_pow₀
Conjugacy in a group with zero
#
source
@[simp]
theorem
GroupWithZero
.
isConj_iff₀
{α :
Type
u_1}
[
GroupWithZero
α
]
{a b :
α
}
:
IsConj
a
b
↔
∃ (
c
:
α
),
c
≠
0
∧
c
*
a
*
c
⁻¹
=
b
source
theorem
GroupWithZero
.
conj_pow₀
{α :
Type
u_1}
[
GroupWithZero
α
]
{s :
ℕ
}
{a d :
α
}
(ha :
a
≠
0
)
:
(
a
⁻¹
*
d
*
a
)
^
s
=
a
⁻¹
*
d
^
s
*
a