← Session 30 — ii′-5e squeeze capstone + 5f perimeter repair
Now the `exists_zero_avoiding_T` adaptation in the same file.
tool: Edit
input
{
"file_path": "D:\\Python\\Quantum\\research\\lean\\NguyenRH1\\NguyenRH1\\LiContour.lean",
"old_string": " have hWFcard : (WF.card : \u211d) \u2264 C0hat (a + 1) := by\n have h1 := hZC a ha\n have h2 : Nat.card (zeroWindow a) = WF.card := by\n rw [Nat.card_coe_set_eq, hWF_def]\n exact Set.ncard_eq_toFinset_card _ hfin\n rw [h2] at h1\n exact h1",
"new_string": " have hWFcard : (WF.card : \u211d) \u2264 C0hat (a + 1) := by\n have h1 := hZC a ha\n -- h1 : ((hfin.toFinset.sum fun \u03c1 => zeroMult \u03c1) : \u211d) \u2264 C0hat (a + 1)\n have h2 : WF.card \u2264 WF.sum (fun \u03c1 => zeroMult \u03c1) := by\n rw [Finset.card_eq_sum_ones]\n apply Finset.sum_le_sum\n intro \u03c1 h\u03c1\n exact one_le_zeroMult ((hWFmem \u03c1).mp h\u03c1).1\n have h3 : (WF.card : \u211d) \u2264 ((WF.sum fun \u03c1 => zeroMult \u03c1) : \u211d) := Nat.cast_le.mpr h2\n exact h3.trans h1"
}
raw content_json (database row)
[{"type":"text","text":"Now the `exists_zero_avoiding_T` adaptation in the same file."},{"type":"tool_use","id":"Edit_96","name":"Edit","input":{"file_path":"D:\\Python\\Quantum\\research\\lean\\NguyenRH1\\NguyenRH1\\LiContour.lean","old_string":" have hWFcard : (WF.card : ℝ) ≤ C0hat (a + 1) := by\n have h1 := hZC a ha\n have h2 : Nat.card (zeroWindow a) = WF.card := by\n rw [Nat.card_coe_set_eq, hWF_def]\n exact Set.ncard_eq_toFinset_card _ hfin\n rw [h2] at h1\n exact h1","new_string":" have hWFcard : (WF.card : ℝ) ≤ C0hat (a + 1) := by\n have h1 := hZC a ha\n -- h1 : ((hfin.toFinset.sum fun ρ => zeroMult ρ) : ℝ) ≤ C0hat (a + 1)\n have h2 : WF.card ≤ WF.sum (fun ρ => zeroMult ρ) := by\n rw [Finset.card_eq_sum_ones]\n apply Finset.sum_le_sum\n intro ρ hρ\n exact one_le_zeroMult ((hWFmem ρ).mp hρ).1\n have h3 : (WF.card : ℝ) ≤ ((WF.sum fun ρ => zeroMult ρ) : ℝ) := Nat.cast_le.mpr h2\n exact h3.trans h1"},"extra_content":null}]