Field instances for ULift

This file defines instances for field, semifield and related structures on ULift types.

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

instance ULift.instRatCastULift {α : Type u} [RatCast α] : RatCast (ULift.{u_1, u} α)

Equations

• ULift.instRatCastULift = { ratCast := fun (a : ℚ) => { down := ↑a } }

@[simp]

theorem ULift.up_ratCast {α : Type u} [RatCast α] (q : ℚ) : { down := ↑q } = ↑q

@[simp]

theorem ULift.down_ratCast {α : Type u} [RatCast α] (q : ℚ) : (↑q).down = ↑q

instance ULift.divisionSemiring {α : Type u} [DivisionSemiring α] : DivisionSemiring (ULift.{u_1, u} α)

Equations

• One or more equations did not get rendered due to their size.

instance ULift.semifield {α : Type u} [Semifield α] : Semifield (ULift.{u_1, u} α)

Equations

• One or more equations did not get rendered due to their size.

instance ULift.divisionRing {α : Type u} [DivisionRing α] : DivisionRing (ULift.{u_1, u} α)

Equations

• One or more equations did not get rendered due to their size.

instance ULift.field {α : Type u} [Field α] : Field (ULift.{u_1, u} α)

Equations

• ULift.field = let src := ULift.semifield; let src_1 := ULift.divisionRing; Field.mk Semifield.zpow (_ : ∀ (a : ULift.{u_1, u} α), a ≠ 0 → a * a⁻¹ = 1) (_ : 0⁻¹ = 0) DivisionRing.qsmul