working…

2024-12-02 17:46:48 +01:00
parent 4320db0533
commit 084841c35a
4 changed files with 77 additions and 66 deletions
--- a/Nevanlinna/laplace.lean
+++ b/Nevanlinna/laplace.lean
@@ -219,6 +219,7 @@ theorem laplace_compCLMAt
    obtain ⟨u, hu₁, hu₂⟩ : ∃ u ∈ nhds x, ContDiffOn ℝ 2 f u := by
      apply ContDiffAt.contDiffOn h
      rfl
+      simp
    obtain ⟨v, hv₁, hv₂, hv₃⟩ := mem_nhds_iff.1 hu₁
    use v
    constructor
--- a/Nevanlinna/partialDeriv.lean
+++ b/Nevanlinna/partialDeriv.lean
@@ -281,7 +281,11 @@ lemma partialDeriv_fderiv {f : E → F} (hf : ContDiff 𝕜 2 f) (z a b : E) :
  unfold partialDeriv
  rw [fderiv_clm_apply]
  · simp
-  · exact (contDiff_succ_iff_fderiv.1 hf).2.differentiable le_rfl z
+  · apply Differentiable.differentiableAt
+    rw [← one_add_one_eq_two] at hf
+    rw [contDiff_succ_iff_fderiv] at hf
+    apply hf.2.2.differentiable
+    simp
  · simp


@@ -298,7 +302,9 @@ lemma partialDeriv_fderivOn
  · simp
  · convert DifferentiableOn.differentiableAt _ (IsOpen.mem_nhds hs hz)
    apply ContDiffOn.differentiableOn _ (Preorder.le_refl 1)
-    exact ((contDiffOn_succ_iff_fderiv_of_isOpen hs).1 hf).2
+    rw [← one_add_one_eq_two] at hf
+    rw [contDiffOn_succ_iff_fderiv_of_isOpen hs] at hf
+    exact hf.2.2
  · simp


@@ -407,7 +413,8 @@ theorem partialDeriv_comm
    let f'' := (fderiv ℝ f' z)
    have h₁ : HasFDerivAt f' f'' z := by
      apply DifferentiableAt.hasFDerivAt
-      apply (contDiff_succ_iff_fderiv.1 h).right.differentiable (Preorder.le_refl 1)
+      rw [← one_add_one_eq_two] at h
+      apply (contDiff_succ_iff_fderiv.1 h).2.2.differentiable (Preorder.le_refl 1)

    apply second_derivative_symmetric h₀ h₁ v₁ v₂

@@ -442,7 +449,8 @@ theorem partialDeriv_commOn
      apply DifferentiableAt.hasFDerivAt
      apply DifferentiableOn.differentiableAt _ (IsOpen.mem_nhds hs hz)
      apply ContDiffOn.differentiableOn _ (Preorder.le_refl 1)
-      exact ((contDiffOn_succ_iff_fderiv_of_isOpen hs).1 h).2
+      rw [← one_add_one_eq_two] at h
+      exact ((contDiffOn_succ_iff_fderiv_of_isOpen hs).1 h).2.2

    have h₀' : ∀ᶠ (y : E) in nhds z, HasFDerivAt f (f' y) y := by
      apply eventually_nhds_iff.mpr
@@ -463,7 +471,9 @@ theorem partialDeriv_commAt
  (h : ContDiffAt ℝ 2 f z) :
  ∀ v₁ v₂ : E, partialDeriv ℝ v₁ (partialDeriv ℝ v₂ f) z = partialDeriv ℝ v₂ (partialDeriv ℝ v₁ f) z := by

-  obtain ⟨u, hu₁, hu₂⟩ := h.contDiffOn le_rfl
+  let A := h.contDiffOn le_rfl
+  simp at A
+  obtain ⟨u, hu₁, hu₂⟩ := A
  obtain ⟨v, hv₁, hv₂, hv₃⟩ := mem_nhds_iff.1 hu₁

  intro v₁ v₂
--- a/lake-manifest.json
+++ b/lake-manifest.json
@@ -1,64 +1,24 @@
 {"version": "1.1.0",
 "packagesDir": ".lake/packages",
 "packages":
- [{"url": "https://github.com/leanprover-community/batteries",
+ [{"url": "https://github.com/leanprover-community/mathlib4.git",
   "type": "git",
   "subDir": null,
-   "scope": "leanprover-community",
-   "rev": "c933dd9b00271d869e22b802a015092d1e8e454a",
-   "name": "batteries",
+   "scope": "",
+   "rev": "7cf807751deab8d4943d867898dc1b31d61b746a",
+   "name": "mathlib",
   "manifestFile": "lake-manifest.json",
-   "inputRev": "main",
-   "inherited": true,
-   "configFile": "lakefile.toml"},
-  {"url": "https://github.com/leanprover-community/quote4",
-   "type": "git",
-   "subDir": null,
-   "scope": "leanprover-community",
-   "rev": "303b23fbcea94ac4f96e590c1cad6618fd4f5f41",
-   "name": "Qq",
-   "manifestFile": "lake-manifest.json",
-   "inputRev": "master",
-   "inherited": true,
+   "inputRev": null,
+   "inherited": false,
   "configFile": "lakefile.lean"},
-  {"url": "https://github.com/leanprover-community/aesop",
+  {"url": "https://github.com/leanprover-community/plausible",
   "type": "git",
   "subDir": null,
   "scope": "leanprover-community",
-   "rev": "de91b59101763419997026c35a41432ac8691f15",
-   "name": "aesop",
+   "rev": "8e5cb8d424df462f84997dd68af6f40e347c3e35",
+   "name": "plausible",
   "manifestFile": "lake-manifest.json",
-   "inputRev": "master",
-   "inherited": true,
-   "configFile": "lakefile.toml"},
-  {"url": "https://github.com/leanprover-community/ProofWidgets4",
-   "type": "git",
-   "subDir": null,
-   "scope": "leanprover-community",
-   "rev": "1383e72b40dd62a566896a6e348ffe868801b172",
-   "name": "proofwidgets",
-   "manifestFile": "lake-manifest.json",
-   "inputRev": "v0.0.46",
-   "inherited": true,
-   "configFile": "lakefile.lean"},
-  {"url": "https://github.com/leanprover/lean4-cli",
-   "type": "git",
-   "subDir": null,
-   "scope": "leanprover",
-   "rev": "726b3c9ad13acca724d4651f14afc4804a7b0e4d",
-   "name": "Cli",
-   "manifestFile": "lake-manifest.json",
-   "inputRev": "main",
-   "inherited": true,
-   "configFile": "lakefile.toml"},
-  {"url": "https://github.com/leanprover-community/import-graph",
-   "type": "git",
-   "subDir": null,
-   "scope": "leanprover-community",
-   "rev": "119b022b3ea88ec810a677888528e50f8144a26e",
-   "name": "importGraph",
-   "manifestFile": "lake-manifest.json",
-   "inputRev": "main",
+   "inputRev": "v4.15.0-rc1",
   "inherited": true,
   "configFile": "lakefile.toml"},
  {"url": "https://github.com/leanprover-community/LeanSearchClient",
@@ -71,25 +31,65 @@
   "inputRev": "main",
   "inherited": true,
   "configFile": "lakefile.toml"},
-  {"url": "https://github.com/leanprover-community/plausible",
+  {"url": "https://github.com/leanprover-community/import-graph",
   "type": "git",
   "subDir": null,
   "scope": "leanprover-community",
-   "rev": "42dc02bdbc5d0c2f395718462a76c3d87318f7fa",
-   "name": "plausible",
+   "rev": "ed3b856bd8893ade75cafe13e8544d4c2660f377",
+   "name": "importGraph",
+   "manifestFile": "lake-manifest.json",
+   "inputRev": "v4.15.0-rc1",
+   "inherited": true,
+   "configFile": "lakefile.toml"},
+  {"url": "https://github.com/leanprover-community/ProofWidgets4",
+   "type": "git",
+   "subDir": null,
+   "scope": "leanprover-community",
+   "rev": "2b000e02d50394af68cfb4770a291113d94801b5",
+   "name": "proofwidgets",
+   "manifestFile": "lake-manifest.json",
+   "inputRev": "v0.0.48",
+   "inherited": true,
+   "configFile": "lakefile.lean"},
+  {"url": "https://github.com/leanprover-community/aesop",
+   "type": "git",
+   "subDir": null,
+   "scope": "leanprover-community",
+   "rev": "8b6048aa0a4a4b6bcf83597802d8dee734e64b7e",
+   "name": "aesop",
+   "manifestFile": "lake-manifest.json",
+   "inputRev": "v4.15.0-rc1",
+   "inherited": true,
+   "configFile": "lakefile.toml"},
+  {"url": "https://github.com/leanprover-community/quote4",
+   "type": "git",
+   "subDir": null,
+   "scope": "leanprover-community",
+   "rev": "ad942fdf0b15c38bface6acbb01d63855a2519ac",
+   "name": "Qq",
+   "manifestFile": "lake-manifest.json",
+   "inputRev": "v4.14.0",
+   "inherited": true,
+   "configFile": "lakefile.lean"},
+  {"url": "https://github.com/leanprover-community/batteries",
+   "type": "git",
+   "subDir": null,
+   "scope": "leanprover-community",
+   "rev": "7805acf1864ba1a2e359f86a8f092ccf1438ad83",
+   "name": "batteries",
   "manifestFile": "lake-manifest.json",
   "inputRev": "main",
   "inherited": true,
   "configFile": "lakefile.toml"},
-  {"url": "https://github.com/leanprover-community/mathlib4.git",
+  {"url": "https://github.com/leanprover/lean4-cli",
   "type": "git",
   "subDir": null,
-   "scope": "",
-   "rev": "ab780650a6c8db2942d137b91ede7c94c47a4950",
-   "name": "mathlib",
+   "scope": "leanprover",
+   "rev": "0c8ea32a15a4f74143e4e1e107ba2c412adb90fd",
+   "name": "Cli",
   "manifestFile": "lake-manifest.json",
-   "inputRev": null,
-   "inherited": false,
-   "configFile": "lakefile.lean"}],
+   "inputRev": "main",
+   "inherited": true,
+   "configFile": "lakefile.toml"}],
 "name": "nevanlinna",
 "lakeDir": ".lake"}
--- a/2
+++ b/2
@@ -1 +1 @@
-leanprover/lean4:v4.14.0-rc3
+leanprover/lean4:v4.15.0-rc1