68 lines
2 KiB
Text
68 lines
2 KiB
Text
set_option synthInstance.etaExperiment true -- TODO: make work by default
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class NonUnitalNonAssocSemiring (α : Type u)
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class NonUnitalSemiring (α : Type u) extends NonUnitalNonAssocSemiring α
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class Semiring (α : Type u) extends NonUnitalSemiring α
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class NonUnitalCommSemiring (α : Type u) extends NonUnitalSemiring α
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class CommSemiring (R : Type u) extends Semiring R
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class NonUnitalNonAssocRing (α : Type u) extends NonUnitalNonAssocSemiring α
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class NonUnitalRing (α : Type _) extends NonUnitalNonAssocRing α, NonUnitalSemiring α
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class Ring (R : Type u) extends Semiring R
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class NonUnitalCommRing (α : Type u) extends NonUnitalRing α
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class CommRing (α : Type u) extends Ring α
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instance (priority := 100) NonUnitalCommRing.toNonUnitalCommSemiring [s : NonUnitalCommRing α] :
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NonUnitalCommSemiring α :=
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{ s with }
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instance (priority := 100) CommRing.toCommSemiring [s : CommRing α] : CommSemiring α :=
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{ s with }
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instance (priority := 100) CommSemiring.toNonUnitalCommSemiring [s : CommSemiring α] :
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NonUnitalCommSemiring α :=
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{ s with }
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instance (priority := 100) CommRing.toNonUnitalCommRing [s : CommRing α] : NonUnitalCommRing α :=
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{ s with }
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class StarRing' (R : Type _) [NonUnitalSemiring R]
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def starGizmo [CommSemiring R] [StarRing' R] : R → R := id
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theorem starGizmo_foo [CommRing R] [StarRing' R] (x : R) : starGizmo x = x := rfl
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namespace ReidMWE
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class A (α : Type u)
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class B (α : Type u) extends A α
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class C (α : Type u) extends B α
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class D (α : Type u) extends B α
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class E (α : Type u) extends C α, D α
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class F (α : Type u) extends A α
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class G (α : Type u) extends F α, B α
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class H (α : Type u) extends C α
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class I (α : Type u) extends G α, D α
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class J (α : Type u) extends H α, I α, E α
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class StarRing' (R : Type 0) [B R]
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def starGizmo [E R] [StarRing' R] : R → R := id
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theorem starGizmo_foo [J R] [StarRing' R] (x : R) : starGizmo x = x := rfl
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theorem T (i : J R) : (@D.toB.{0} R (@E.toD.{0} R (@J.toE.{0} R i))) = i.toB := rfl
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