ULift instances for ring

This file defines instances for ring, semiring and related structures on ULift types.

(Recall ULift R is just a "copy" of a type R in a higher universe.)

We also provide ULift.ringEquiv : ULift R ≃+* R.

instance ULift.mulZeroClass {M₀ : Type u_1} [MulZeroClass M₀] : MulZeroClass (ULift.{u_2, u_1} M₀)

instance ULift.distrib {R : Type u} [Distrib R] : Distrib (ULift.{u_1, u} R)

instance ULift.instNatCast {R : Type u} [NatCast R] : NatCast (ULift.{u_1, u} R)

instance ULift.instIntCast {R : Type u} [IntCast R] : IntCast (ULift.{u_1, u} R)

@[simp]

theorem ULift.up_natCast {R : Type u} [NatCast R] (n : ℕ) : { down := ↑n } = ↑n

@[simp]

theorem ULift.up_ofNat {R : Type u} [NatCast R] (n : ℕ) [n.AtLeastTwo] : { down := OfNat.ofNat n } = OfNat.ofNat n

@[simp]

theorem ULift.up_intCast {R : Type u} [IntCast R] (n : ℤ) : { down := ↑n } = ↑n

@[simp]

theorem ULift.down_natCast {R : Type u} [NatCast R] (n : ℕ) : (↑n).down = ↑n

@[simp]

theorem ULift.down_ofNat {R : Type u} [NatCast R] (n : ℕ) [n.AtLeastTwo] : (OfNat.ofNat n).down = OfNat.ofNat n

@[simp]

theorem ULift.down_intCast {R : Type u} [IntCast R] (n : ℤ) : (↑n).down = ↑n

instance ULift.addMonoidWithOne {R : Type u} [AddMonoidWithOne R] : AddMonoidWithOne (ULift.{u_1, u} R)

instance ULift.addCommMonoidWithOne {R : Type u} [AddCommMonoidWithOne R] : AddCommMonoidWithOne (ULift.{u_1, u} R)

instance ULift.addGroupWithOne {R : Type u} [AddGroupWithOne R] : AddGroupWithOne (ULift.{u_1, u} R)

instance ULift.addCommGroupWithOne {R : Type u} [AddCommGroupWithOne R] : AddCommGroupWithOne (ULift.{u_1, u} R)

instance ULift.nonUnitalNonAssocSemiring {R : Type u} [NonUnitalNonAssocSemiring R] : NonUnitalNonAssocSemiring (ULift.{u_1, u} R)

instance ULift.nonAssocSemiring {R : Type u} [NonAssocSemiring R] : NonAssocSemiring (ULift.{u_1, u} R)

instance ULift.nonUnitalSemiring {R : Type u} [NonUnitalSemiring R] : NonUnitalSemiring (ULift.{u_1, u} R)

instance ULift.semiring {R : Type u} [Semiring R] : Semiring (ULift.{u_1, u} R)

def ULift.ringEquiv {R : Type u} [NonUnitalNonAssocSemiring R] : ULift.{u_1, u} R ≃+* R

The ring equivalence between ULift R and R.

instance ULift.nonUnitalCommSemiring {R : Type u} [NonUnitalCommSemiring R] : NonUnitalCommSemiring (ULift.{u_1, u} R)

instance ULift.commSemiring {R : Type u} [CommSemiring R] : CommSemiring (ULift.{u_1, u} R)

instance ULift.nonUnitalNonAssocRing {R : Type u} [NonUnitalNonAssocRing R] : NonUnitalNonAssocRing (ULift.{u_1, u} R)

instance ULift.nonUnitalRing {R : Type u} [NonUnitalRing R] : NonUnitalRing (ULift.{u_1, u} R)

instance ULift.nonAssocRing {R : Type u} [NonAssocRing R] : NonAssocRing (ULift.{u_1, u} R)

instance ULift.ring {R : Type u} [Ring R] : Ring (ULift.{u_1, u} R)

instance ULift.nonUnitalCommRing {R : Type u} [NonUnitalCommRing R] : NonUnitalCommRing (ULift.{u_1, u} R)

instance ULift.commRing {R : Type u} [CommRing R] : CommRing (ULift.{u_1, u} R)