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Mathlib
.
Algebra
.
Star
.
Rat
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Imports
Init
Mathlib.Algebra.Field.Opposite
Mathlib.Algebra.Star.Basic
Mathlib.Data.NNRat.Defs
Mathlib.Data.Rat.Cast.Defs
Imported by
Rat
.
instStarRing
NNRat
.
instStarRing
Rat
.
instTrivialStar
NNRat
.
instTrivialStar
star_nnratCast
star_ratCast
*-ring structure on ℚ and ℚ≥0.
#
source
instance
Rat
.
instStarRing
:
StarRing
ℚ
Equations
Rat.instStarRing
=
starRingOfComm
source
instance
NNRat
.
instStarRing
:
StarRing
ℚ≥0
Equations
NNRat.instStarRing
=
starRingOfComm
source
instance
Rat
.
instTrivialStar
:
TrivialStar
ℚ
Equations
Rat.instTrivialStar
=
⋯
source
instance
NNRat
.
instTrivialStar
:
TrivialStar
ℚ≥0
Equations
NNRat.instTrivialStar
=
⋯
source
@[simp]
theorem
star_nnratCast
{R :
Type
u_1}
[
DivisionSemiring
R
]
[
StarRing
R
]
(q :
ℚ≥0
)
:
star
↑
q
=
↑
q
source
@[simp]
theorem
star_ratCast
{R :
Type
u_1}
[
DivisionRing
R
]
[
StarRing
R
]
(r :
ℚ
)
:
star
↑
r
=
↑
r