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| 1 | +class NonUnitalNonAssocSemiring (α : Type u) |
| 2 | + |
| 3 | +class NonUnitalSemiring (α : Type u) extends NonUnitalNonAssocSemiring α |
| 4 | + |
| 5 | +class Semiring (α : Type u) extends NonUnitalSemiring α |
| 6 | + |
| 7 | +class NonUnitalCommSemiring (α : Type u) extends NonUnitalSemiring α |
| 8 | + |
| 9 | +class CommSemiring (R : Type u) extends Semiring R |
| 10 | + |
| 11 | +class NonUnitalNonAssocRing (α : Type u) extends NonUnitalNonAssocSemiring α |
| 12 | + |
| 13 | +class NonUnitalRing (α : Type _) extends NonUnitalNonAssocRing α, NonUnitalSemiring α |
| 14 | + |
| 15 | +class Ring (R : Type u) extends Semiring R |
| 16 | + |
| 17 | +class NonUnitalCommRing (α : Type u) extends NonUnitalRing α |
| 18 | + |
| 19 | +class CommRing (α : Type u) extends Ring α |
| 20 | + |
| 21 | +instance (priority := 100) NonUnitalCommRing.toNonUnitalCommSemiring [s : NonUnitalCommRing α] : |
| 22 | + NonUnitalCommSemiring α := |
| 23 | + { s with } |
| 24 | + |
| 25 | +instance (priority := 100) CommRing.toCommSemiring [s : CommRing α] : CommSemiring α := |
| 26 | + { s with } |
| 27 | + |
| 28 | +instance (priority := 100) CommSemiring.toNonUnitalCommSemiring [s : CommSemiring α] : |
| 29 | + NonUnitalCommSemiring α := |
| 30 | + { s with } |
| 31 | + |
| 32 | +instance (priority := 100) CommRing.toNonUnitalCommRing [s : CommRing α] : NonUnitalCommRing α := |
| 33 | + { s with } |
| 34 | + |
| 35 | +class StarRing' (R : Type _) [NonUnitalSemiring R] |
| 36 | +def starGizmo [CommSemiring R] [StarRing' R] : R → R := id |
| 37 | +theorem starGizmo_foo [CommRing R] [StarRing' R] (x : R) : starGizmo x = x := rfl |
| 38 | + |
| 39 | +namespace ReidMWE |
| 40 | + |
| 41 | +class A (α : Type u) |
| 42 | + |
| 43 | +class B (α : Type u) extends A α |
| 44 | + |
| 45 | +class C (α : Type u) extends B α |
| 46 | + |
| 47 | +class D (α : Type u) extends B α |
| 48 | + |
| 49 | +class E (α : Type u) extends C α, D α |
| 50 | + |
| 51 | +class F (α : Type u) extends A α |
| 52 | + |
| 53 | +class G (α : Type u) extends F α, B α |
| 54 | + |
| 55 | +class H (α : Type u) extends C α |
| 56 | + |
| 57 | +class I (α : Type u) extends G α, D α |
| 58 | + |
| 59 | +class J (α : Type u) extends H α, I α, E α |
| 60 | + |
| 61 | +class StarRing' (R : Type 0) [B R] |
| 62 | +def starGizmo [E R] [StarRing' R] : R → R := id |
| 63 | + |
| 64 | +theorem starGizmo_foo [J R] [StarRing' R] (x : R) : starGizmo x = x := rfl |
| 65 | + |
| 66 | +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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