← Session 17 — Lean tier (i): elementary proofs (after crash)
thinking (413 chars)
I made a mistake — `h1.self_of_nhdsWithin??` is not valid; I left a placeholder. For hd1: from h1 (eventually HasDerivAt), the point-instance at T: `h1.self_of_nhds` : HasDerivAt φ (D1 T) T — `Filter.Eventually.self_of_nhds : (∀ᶠ x in 𝓝 T, p x) → p T` ✓. So hd1 := h1.self_of_nhds.deriv. Let me fix that line and remove the sorry, completing the lemma (ψ = −1/(T+2)² − (T+2)⁻¹/(T−1) → massage to the stated form).
Fixing the placeholder I left in `psiOf_log_shift`.
tool: Edit
input
{
"file_path": "D:\\Python\\Quantum\\research\\lean\\NguyenRH1\\NguyenRH1\\LiSkeleton.lean",
"old_string": " have hd2 := deriv2_of_hasDerivAt_nhds h1 h2\n have hd1 : deriv (fun t => Real.log (t + 2)) T = (T + 2)\u207b\u00b9 :=\n (h1.self_of_nhdsWithin??).deriv\n sorry",
"new_string": " have hd2 := deriv2_of_hasDerivAt_nhds h1 h2\n have hd1 : deriv (fun t => Real.log (t + 2)) T = (T + 2)\u207b\u00b9 := h1.self_of_nhds.deriv\n unfold psiOf\n rw [hd2, hd1]\n have hT1 : (T - 1) \u2260 0 := by linarith\n field_simp [hT2.ne']\n ring"
}
raw content_json (database row)
[{"type":"thinking","thinking":"I made a mistake — `h1.self_of_nhdsWithin??` is not valid; I left a placeholder. For hd1: from h1 (eventually HasDerivAt), the point-instance at T: `h1.self_of_nhds` : HasDerivAt φ (D1 T) T — `Filter.Eventually.self_of_nhds : (∀ᶠ x in 𝓝 T, p x) → p T` ✓. So hd1 := h1.self_of_nhds.deriv. Let me fix that line and remove the sorry, completing the lemma (ψ = −1/(T+2)² − (T+2)⁻¹/(T−1) → massage to the stated form).","signature":""},{"type":"text","text":"Fixing the placeholder I left in `psiOf_log_shift`."},{"type":"tool_use","id":"Edit_99","name":"Edit","input":{"file_path":"D:\\Python\\Quantum\\research\\lean\\NguyenRH1\\NguyenRH1\\LiSkeleton.lean","old_string":" have hd2 := deriv2_of_hasDerivAt_nhds h1 h2\n have hd1 : deriv (fun t => Real.log (t + 2)) T = (T + 2)⁻¹ :=\n (h1.self_of_nhdsWithin??).deriv\n sorry","new_string":" have hd2 := deriv2_of_hasDerivAt_nhds h1 h2\n have hd1 : deriv (fun t => Real.log (t + 2)) T = (T + 2)⁻¹ := h1.self_of_nhds.deriv\n unfold psiOf\n rw [hd2, hd1]\n have hT1 : (T - 1) ≠ 0 := by linarith\n field_simp [hT2.ne']\n ring"},"extra_content":null}]