36 lines
1.2 KiB
Plaintext
36 lines
1.2 KiB
Plaintext
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import Mathlib.Analysis.Calculus.ContDiff.Basic
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import Mathlib.Analysis.Calculus.FDeriv.Add
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variable {𝕜 : Type*} [NontriviallyNormedField 𝕜]
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variable {E : Type*} [NormedAddCommGroup E] [NormedSpace 𝕜 E]
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variable {F : Type*} [NormedAddCommGroup F] [NormedSpace 𝕜 F]
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variable {G : Type*} [NormedAddCommGroup G] [NormedSpace 𝕜 G]
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variable {G' : Type*} [NormedAddCommGroup G'] [NormedSpace 𝕜 G']
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variable {f f₀ f₁ g : E → F}
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variable {f' f₀' f₁' g' : E →L[𝕜] F}
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variable (e : E →L[𝕜] F)
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variable {x : E}
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variable {s t : Set E}
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variable {L L₁ L₂ : Filter E}
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variable {R : Type*} [Semiring R] [Module R F] [SMulCommClass 𝕜 R F] [ContinuousConstSMul R F]
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-- import Mathlib.Analysis.Calculus.FDeriv.Add
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@[fun_prop]
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theorem Differentiable.const_smul' (h : Differentiable 𝕜 f) (c : R) :
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Differentiable 𝕜 (c • f) := by
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have : c • f = fun x ↦ c • f x := rfl
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rw [this]
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exact Differentiable.const_smul h c
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-- Mathlib.Analysis.Calculus.ContDiff.Basic
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theorem ContDiff.const_smul' {f : E → F} (c : R) (hf : ContDiff 𝕜 n f) :
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ContDiff 𝕜 n (c • f) := by
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have : c • f = fun x ↦ c • f x := rfl
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rw [this]
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exact ContDiff.const_smul c hf
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