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Imports
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Mathlib.Algebra.Order.Group.Abs
Mathlib.Algebra.Order.Monoid.Submonoid
Mathlib.Algebra.Order.Ring.Basic
Mathlib.Algebra.Order.Ring.Int
Mathlib.Algebra.Order.Star.Basic
Imported by
Int
.
addSubmonoid_closure_range_pow
Int
.
addSubmonoid_closure_range_mul_self
Int
.
instStarOrderedRing
Star ordered ring structure on
ℤ
#
This file shows that
ℤ
is a
StarOrderedRing
.
source
@[simp]
theorem
Int
.
addSubmonoid_closure_range_pow
{
n
:
ℕ
}
(
hn
:
Even
n
)
:
AddSubmonoid.closure
(
Set.range
fun (
x
:
ℤ
) =>
x
^
n
)
=
AddSubmonoid.nonneg
ℤ
source
@[simp]
theorem
Int
.
addSubmonoid_closure_range_mul_self
:
AddSubmonoid.closure
(
Set.range
fun (
x
:
ℤ
) =>
x
*
x
)
=
AddSubmonoid.nonneg
ℤ
source
instance
Int
.
instStarOrderedRing
:
StarOrderedRing
ℤ