File: Mathlib/Algebra/Ring/Subsemiring/Order.lean

full_name: SubsemiringClass.toOrderedSemiring
code: /-- A subsemiring of an `OrderedSemiring` is an `OrderedSemiring`. -/
instance toOrderedSemiring [OrderedSemiring R] [SubsemiringClass S R] :
    OrderedSemiring s 
goal: OrderedSemiring ↥s

full_name: SubsemiringClass.toStrictOrderedSemiring
code: /-- A subsemiring of a `StrictOrderedSemiring` is a `StrictOrderedSemiring`. -/
instance toStrictOrderedSemiring [StrictOrderedSemiring R]
    [SubsemiringClass S R] : StrictOrderedSemiring s 
goal: StrictOrderedSemiring ↥s

full_name: SubsemiringClass.toOrderedCommSemiring
code: /-- A subsemiring of an `OrderedCommSemiring` is an `OrderedCommSemiring`. -/
instance toOrderedCommSemiring [OrderedCommSemiring R] [SubsemiringClass S R] :
    OrderedCommSemiring s 
goal: OrderedCommSemiring ↥s

full_name: SubsemiringClass.toStrictOrderedCommSemiring
code: /-- A subsemiring of a `StrictOrderedCommSemiring` is a `StrictOrderedCommSemiring`. -/
instance toStrictOrderedCommSemiring [StrictOrderedCommSemiring R]
    [SubsemiringClass S R] : StrictOrderedCommSemiring s 
goal: StrictOrderedCommSemiring ↥s

full_name: SubsemiringClass.toLinearOrderedSemiring
code: /-- A subsemiring of a `LinearOrderedSemiring` is a `LinearOrderedSemiring`. -/
instance toLinearOrderedSemiring [LinearOrderedSemiring R]
    [SubsemiringClass S R] : LinearOrderedSemiring s 
goal: LinearOrderedSemiring ↥s

full_name: SubsemiringClass.toLinearOrderedCommSemiring
code: /-- A subsemiring of a `LinearOrderedCommSemiring` is a `LinearOrderedCommSemiring`. -/
instance toLinearOrderedCommSemiring [LinearOrderedCommSemiring R]
    [SubsemiringClass S R] : LinearOrderedCommSemiring s 
goal: LinearOrderedCommSemiring ↥s

full_name: Subsemiring.toOrderedSemiring
code: /-- A subsemiring of an `OrderedSemiring` is an `OrderedSemiring`. -/
instance toOrderedSemiring [OrderedSemiring R] (s : Subsemiring R) : OrderedSemiring s 
goal: OrderedSemiring ↥s

full_name: Subsemiring.toStrictOrderedSemiring
code: /-- A subsemiring of a `StrictOrderedSemiring` is a `StrictOrderedSemiring`. -/
instance toStrictOrderedSemiring [StrictOrderedSemiring R] (s : Subsemiring R) :
    StrictOrderedSemiring s 
goal: StrictOrderedSemiring ↥s

full_name: Subsemiring.toOrderedCommSemiring
code: /-- A subsemiring of an `OrderedCommSemiring` is an `OrderedCommSemiring`. -/
instance toOrderedCommSemiring [OrderedCommSemiring R] (s : Subsemiring R) :
    OrderedCommSemiring s 
goal: OrderedCommSemiring ↥s

full_name: Subsemiring.toStrictOrderedCommSemiring
code: /-- A subsemiring of a `StrictOrderedCommSemiring` is a `StrictOrderedCommSemiring`. -/
instance toStrictOrderedCommSemiring [StrictOrderedCommSemiring R] (s : Subsemiring R) :
    StrictOrderedCommSemiring s 
goal: StrictOrderedCommSemiring ↥s

full_name: Subsemiring.toLinearOrderedSemiring
code: /-- A subsemiring of a `LinearOrderedSemiring` is a `LinearOrderedSemiring`. -/
instance toLinearOrderedSemiring [LinearOrderedSemiring R] (s : Subsemiring R) :
    LinearOrderedSemiring s 
goal: LinearOrderedSemiring ↥s

full_name: Subsemiring.toLinearOrderedCommSemiring
code: /-- A subsemiring of a `LinearOrderedCommSemiring` is a `LinearOrderedCommSemiring`. -/
instance toLinearOrderedCommSemiring [LinearOrderedCommSemiring R] (s : Subsemiring R) :
    LinearOrderedCommSemiring s 
goal: LinearOrderedCommSemiring ↥s

full_name: Subsemiring.nonneg_carrier
code: /-- The set of nonnegative elements in an ordered semiring, as a subsemiring. -/
@[simps]
def nonneg (R : Type*) [OrderedSemiring R] : Subsemiring R 
goal: ↑(Subsemiring.nonneg R) = Set.Ici 0

full_name: Subsemiring.nonneg
code: /-- The set of nonnegative elements in an ordered semiring, as a subsemiring. -/
@[simps]
def nonneg (R : Type*) [OrderedSemiring R] : Subsemiring R 
goal: Subsemiring R