From 084841c35a4cc82b9eb43b5c20dae630eda1da4a Mon Sep 17 00:00:00 2001 From: Stefan Kebekus Date: Mon, 2 Dec 2024 17:46:48 +0100 Subject: [PATCH] =?UTF-8?q?working=E2=80=A6?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- Nevanlinna/laplace.lean | 1 + Nevanlinna/partialDeriv.lean | 20 ++++-- lake-manifest.json | 120 +++++++++++++++++------------------ lean-toolchain | 2 +- 4 files changed, 77 insertions(+), 66 deletions(-) diff --git a/Nevanlinna/laplace.lean b/Nevanlinna/laplace.lean index d85b4d0..1df6769 100644 --- 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 diff --git a/Nevanlinna/partialDeriv.lean b/Nevanlinna/partialDeriv.lean index 754d10f..05c1c44 100644 --- 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 diff --git a/lake-manifest.json b/lake-manifest.json index 722921e..fe71dbe 100644 --- 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"} diff --git a/lean-toolchain b/lean-toolchain index 6d9e70f..cf25a98 100644 --- a/lean-toolchain +++ b/lean-toolchain @@ -1 +1 @@ -leanprover/lean4:v4.14.0-rc3 +leanprover/lean4:v4.15.0-rc1