a440e63435
Closes #3705 This PR also fixes a performance issue at `ACLt` also exposed by example at #3705
34 lines
1.3 KiB
Text
34 lines
1.3 KiB
Text
structure MonoidHom (M : Type _) (N : Type _) [Mul M] [Mul N] where
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toFun : M → N
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map_mul' : ∀ x y, toFun (x * y) = toFun x * toFun y
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class CommMagma (G : Type _) extends Mul G where
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mul_comm : ∀ a b : G, a * b = b * a
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set_option quotPrecheck false
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infixr:25 " →*' " => MonoidHom
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instance [Mul M] [Mul N] : CoeFun (M →*' N) (fun _ => M → N) where
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coe := MonoidHom.toFun
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open CommMagma
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-- -- this instance needed
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instance MonoidHom.commMonoid [Mul M] [Mul N] :
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CommMagma (M →*' N) where
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mul := fun f g => { toFun := fun x => f x * g x, map_mul' := sorry }
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mul_comm := sorry
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example {M} [Mul M] [Mul G] [Pow G Int] :
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let zpow : Int → (M →*' G) → (M →*' G) := fun n f => { toFun := fun x => f x ^ n, map_mul' := sorry }
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∀ (n : Nat) (a : M →*' G), zpow (Int.ofNat (Nat.succ n)) a = a * zpow (Int.ofNat n) a := by
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simp only [Int.ofNat_eq_coe] -- commenting out this line makes simp loop
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simp (config := { failIfUnchanged := false }) only [mul_comm] -- should not produce: unexpected bound variable 2
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sorry
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theorem ex₂ {M} [Mul M] [Mul G] [Pow G Int] :
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let zpow : Int → (M →*' G) → (M →*' G) := fun n f => { toFun := fun x => f x ^ n, map_mul' := sorry }
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∀ (n : Nat) (a : M →*' G), zpow (Int.ofNat (Nat.succ n)) a = a * zpow (Int.ofNat n) a := by
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simp only [mul_comm]
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sorry
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