20 lines
660 B
Text
20 lines
660 B
Text
class Vec (X : Type) extends Add X, Inhabited X
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class Vec' (X : Type) extends Vec X
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def differential {X Y : Type} [Vec X] [Vec Y] (f : X → Y) (x dx : X) : Y := f dx
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@[simp]
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theorem differential_of_linear {X Y : Type} [Vec X] [Vec Y] (f : X → Y) (x dx : X)
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: differential f x dx = f dx := by simp[differential]
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example {X Y : Type} [Vec X] [Vec Y] (f : X → Y) (x dx : X)
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: differential f x dx = f dx := by simp
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instance : Vec Nat := ⟨⟩
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instance : Vec' Nat := ⟨⟩
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set_option trace.Meta.Tactic.simp true
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example {Y : Type} [Vec Y] (f : Nat → Y) (x dx : Nat)
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: @differential _ _ Vec'.toVec _ f x dx = f dx :=
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by simp
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