113 lines
3.3 KiB
Text
113 lines
3.3 KiB
Text
/-!
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This is a minimization of an issue widely seen in Mathlib after
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https://github.com/leanprover/lean4/pull/2793.
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We find that we need to either specify a named argument or use `..` in certain rewrites.
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-/
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section Mathlib.Data.FunLike.Basic
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class DFunLike (F : Sort _) (α : outParam (Sort _)) (β : outParam <| α → Sort _) where
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coe : F → ∀ a : α, β a
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abbrev FunLike F α β := DFunLike F α fun _ => β
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instance (priority := 100) hasCoeToFun {F α β} [_i : DFunLike F α β] :
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CoeFun F (fun _ ↦ ∀ a : α, β a) where
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coe := @DFunLike.coe _ _ β _
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end Mathlib.Data.FunLike.Basic
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section Mathlib.Algebra.Group.Hom.Defs
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variable {M N : Type _}
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variable {F : Type _}
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class ZeroHomClass (F : Type _) (M N : outParam (Type _)) [Zero M] [Zero N] [FunLike F M N] :
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Prop where
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map_zero : ∀ f : F, f 0 = 0
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variable [Zero M] [Zero N] [FunLike F M N]
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theorem map_zero [ZeroHomClass F M N] (f : F) : f 0 = 0 :=
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ZeroHomClass.map_zero f
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end Mathlib.Algebra.Group.Hom.Defs
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section Mathlib.GroupTheory.GroupAction.Defs
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variable {M A : Type _}
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class SMulZeroClass (M A : Type _) [Zero A] extends SMul M A where
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smul_zero : ∀ a : M, a • (0 : A) = 0
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@[simp]
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theorem smul_zero [Zero A] [SMulZeroClass M A] (a : M) : a • (0 : A) = 0 :=
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SMulZeroClass.smul_zero _
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end Mathlib.GroupTheory.GroupAction.Defs
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section Mathlib.Algebra.SMulWithZero
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variable (R M)
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class SMulWithZero [Zero R] [Zero M] extends SMulZeroClass R M where
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@[simp]
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theorem zero_smul {M} [Zero R] [Zero M] [SMulWithZero R M] (m : M) : (0 : R) • m = 0 := sorry
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end Mathlib.Algebra.SMulWithZero
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section Mathlib.GroupTheory.GroupAction.Hom
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class MulActionSemiHomClass (F : Type _)
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{M N : outParam (Type _)} (φ : outParam (M → N))
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(X Y : outParam (Type _)) [SMul M X] [SMul N Y] [FunLike F X Y] : Prop where
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map_smulₛₗ : ∀ (f : F) (c : M) (x : X), f (c • x) = (φ c) • (f x)
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export MulActionSemiHomClass (map_smulₛₗ)
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end Mathlib.GroupTheory.GroupAction.Hom
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section Mathlib.Algebra.Module.LinearMap.Defs
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variable {R S S₃ T M M₃ : Type _}
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class LinearMapClass (F : Type _) (R : outParam (Type _))
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(M M₂ : outParam (Type _)) [Add M] [Add M₂]
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[SMul R M] [SMul R M₂] [FunLike F M M₂] : Prop
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extends MulActionSemiHomClass F (id : R → R) M M₂
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variable (F : Type _)
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variable [Zero R]
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variable [Zero M] [Add M] [Zero M₃] [Add M₃]
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variable [SMulWithZero R M] [SMulWithZero R M₃]
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def inst1 [FunLike F M M₃] [LinearMapClass F R M M₃] : ZeroHomClass F M M₃ :=
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{ map_zero := fun f ↦
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show f 0 = 0 by
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rw [← zero_smul R (0 : M), @map_smulₛₗ]
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simp only [id_eq, zero_smul]
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}
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def inst2 [FunLike F M M₃] [LinearMapClass F R M M₃] : ZeroHomClass F M M₃ :=
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{ map_zero := fun f ↦
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show f 0 = 0 by
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rw [← zero_smul R (0 : M), map_smulₛₗ (N := R)]
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simp only [id_eq, zero_smul]
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}
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def inst3 [FunLike F M M₃] [LinearMapClass F R M M₃] : ZeroHomClass F M M₃ :=
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{ map_zero := fun f ↦
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show f 0 = 0 by
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rw [← zero_smul R (0 : M), map_smulₛₗ ]
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simp only [id_eq, zero_smul]
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}
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def inst4 [FunLike F M M₃] [LinearMapClass F R M M₃] : ZeroHomClass F M M₃ :=
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{ map_zero := fun f ↦
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show f 0 = 0 by
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rw [← zero_smul R (0 : M), map_smulₛₗ ..]
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simp only [id_eq, zero_smul]
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}
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end Mathlib.Algebra.Module.LinearMap.Defs
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