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@ -297,7 +297,7 @@ lemma partialDeriv_fderivOn
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rw [fderiv_clm_apply]
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rw [fderiv_clm_apply]
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· simp
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· simp
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· convert DifferentiableOn.differentiableAt _ (IsOpen.mem_nhds hs hz)
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· convert DifferentiableOn.differentiableAt _ (IsOpen.mem_nhds hs hz)
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apply ContDiffOn.differentiableOn _ (Submonoid.oneLE.proof_2 ℕ∞)
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apply ContDiffOn.differentiableOn _ (Preorder.le_refl 1)
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exact ((contDiffOn_succ_iff_fderiv_of_isOpen hs).1 hf).2
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exact ((contDiffOn_succ_iff_fderiv_of_isOpen hs).1 hf).2
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· simp
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· simp
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@ -407,7 +407,7 @@ theorem partialDeriv_comm
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let f'' := (fderiv ℝ f' z)
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let f'' := (fderiv ℝ f' z)
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have h₁ : HasFDerivAt f' f'' z := by
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have h₁ : HasFDerivAt f' f'' z := by
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apply DifferentiableAt.hasFDerivAt
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apply DifferentiableAt.hasFDerivAt
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apply (contDiff_succ_iff_fderiv.1 h).right.differentiable (Submonoid.oneLE.proof_2 ℕ∞)
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apply (contDiff_succ_iff_fderiv.1 h).right.differentiable (Preorder.le_refl 1)
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apply second_derivative_symmetric h₀ h₁ v₁ v₂
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apply second_derivative_symmetric h₀ h₁ v₁ v₂
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@ -441,7 +441,7 @@ theorem partialDeriv_commOn
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have h₁ : HasFDerivAt f' f'' z := by
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have h₁ : HasFDerivAt f' f'' z := by
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apply DifferentiableAt.hasFDerivAt
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apply DifferentiableAt.hasFDerivAt
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apply DifferentiableOn.differentiableAt _ (IsOpen.mem_nhds hs hz)
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apply DifferentiableOn.differentiableAt _ (IsOpen.mem_nhds hs hz)
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apply ContDiffOn.differentiableOn _ (Submonoid.oneLE.proof_2 ℕ∞)
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apply ContDiffOn.differentiableOn _ (Preorder.le_refl 1)
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exact ((contDiffOn_succ_iff_fderiv_of_isOpen hs).1 h).2
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exact ((contDiffOn_succ_iff_fderiv_of_isOpen hs).1 h).2
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have h₀' : ∀ᶠ (y : E) in nhds z, HasFDerivAt f (f' y) y := by
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have h₀' : ∀ᶠ (y : E) in nhds z, HasFDerivAt f (f' y) y := by
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@ -5,7 +5,7 @@
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"type": "git",
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"type": "git",
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"subDir": null,
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"subDir": null,
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"scope": "leanprover-community",
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"scope": "leanprover-community",
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"rev": "d747f070e42dd21e2649b75090f5b0d45c6ec8e0",
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"rev": "8feac540abb781cb1349688c816dc02fae66b49c",
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"name": "batteries",
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"name": "batteries",
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"manifestFile": "lake-manifest.json",
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"manifestFile": "lake-manifest.json",
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"inputRev": "main",
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"inputRev": "main",
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@ -15,7 +15,7 @@
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"type": "git",
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"type": "git",
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"subDir": null,
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"subDir": null,
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"scope": "leanprover-community",
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"scope": "leanprover-community",
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"rev": "71f54425e6fe0fa75f3aef33a2813a7898392222",
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"rev": "2c8ae451ce9ffc83554322b14437159c1a9703f9",
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"name": "Qq",
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"name": "Qq",
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"manifestFile": "lake-manifest.json",
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"manifestFile": "lake-manifest.json",
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"inputRev": "master",
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"inputRev": "master",
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@ -25,7 +25,7 @@
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"type": "git",
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"type": "git",
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"subDir": null,
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"subDir": null,
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"scope": "leanprover-community",
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"scope": "leanprover-community",
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"rev": "c792cfd1efe6e01cb176e158ddb195bedfb7ad33",
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"rev": "e291aa4de57079b3d2199b9eb7b4b00922b85a7c",
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"name": "aesop",
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"name": "aesop",
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"manifestFile": "lake-manifest.json",
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"manifestFile": "lake-manifest.json",
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"inputRev": "master",
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"inputRev": "master",
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@ -35,10 +35,10 @@
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"type": "git",
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"type": "git",
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"subDir": null,
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"subDir": null,
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"scope": "leanprover-community",
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"scope": "leanprover-community",
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"rev": "a96aee5245720f588876021b6a0aa73efee49c76",
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"rev": "eb08eee94098fe530ccd6d8751a86fe405473d4c",
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"name": "proofwidgets",
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"name": "proofwidgets",
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"manifestFile": "lake-manifest.json",
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"manifestFile": "lake-manifest.json",
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"inputRev": "v0.0.41",
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"inputRev": "v0.0.42",
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"inherited": true,
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"inherited": true,
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"configFile": "lakefile.lean"},
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"configFile": "lakefile.lean"},
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{"url": "https://github.com/leanprover/lean4-cli",
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{"url": "https://github.com/leanprover/lean4-cli",
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@ -55,7 +55,7 @@
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"type": "git",
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"type": "git",
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"subDir": null,
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"subDir": null,
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"scope": "leanprover-community",
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"scope": "leanprover-community",
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"rev": "57bd2065f1dbea5e9235646fb836c7cea9ab03b6",
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"rev": "fb7841a6f4fb389ec0e47dd4677844d49906af3c",
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"name": "importGraph",
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"name": "importGraph",
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"manifestFile": "lake-manifest.json",
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"manifestFile": "lake-manifest.json",
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"inputRev": "main",
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"inputRev": "main",
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@ -65,7 +65,7 @@
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"type": "git",
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"type": "git",
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"subDir": null,
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"subDir": null,
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"scope": "",
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"scope": "",
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"rev": "cae1b27ace5330f372b57f1051e228fe9b264d57",
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"rev": "8c811c94af285516e8c76a63165c87027f18ccd0",
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"name": "mathlib",
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"name": "mathlib",
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"manifestFile": "lake-manifest.json",
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"manifestFile": "lake-manifest.json",
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"inputRev": null,
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"inputRev": null,
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@ -1 +1 @@
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leanprover/lean4:v4.11.0-rc2
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leanprover/lean4:v4.12.0-rc1
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