← Session 18 — Lean tier (ii): finite-height proof + certified base points
thinking (518 chars)
It's `ConvexOn.subset (hf : ConvexOn 𝕜 t f) (hst : s ⊆ t) (hs : Convex 𝕜 s) : ConvexOn 𝕜 s f`. So:
```
have hconv' : ConvexOn ℝ (Set.Ici N₀) f :=
hconv.subset (Set.Ici_subset_Ici.mpr (le_of_lt hN)) (convex_Ici N₀)
```
Now apply all fixes:
1. Line ~50-56: docstring → plain comment.
2. marginTilde_eq_sub: drop ring.
3. hD2: convert → e/rwa pattern.
4. Delete bogus h2 block.
5. pos_of_convex_of_base: rw [heq] → rw [← heq]; hfc restructure; hconv.mono → hconv.subset ... (convex_Ici _).
6. FAlt_psi_neg: {T} → (T).
It's `ConvexOn.subset` with an explicit convexity argument. Applying all fixes now.
tool: Edit
input
{
"file_path": "D:\\Python\\Quantum\\research\\lean\\NguyenRH1\\NguyenRH1\\LiSkeleton.lean",
"old_string": "/-- [PROVED session 012, tier (ii) step 1 \u2014 assembly modulo the named\nanalytic hypothesis] R-004, the finite-height Li theorem (draft Thm 3.1).\nThe full statement and proof are at the END of this file (\u00a74), after the\nmargin machinery they depend on: `lambda_pos_finite_height` there is\nproved from `SfBoundProp` (the single named analytic hypothesis, D-062\ntriage) + the computational perimeter (Platt\u2013Trudgian `RHUpTo`,\n`LiVerifiedUpTo`) + two elementary base-point evaluations. -/",
"new_string": "/- [PROVED session 012, tier (ii) step 1 \u2014 assembly modulo the named\nanalytic hypothesis] R-004, the finite-height Li theorem (draft Thm 3.1).\nThe full statement and proof are at the END of this file (\u00a74), after the\nmargin machinery they depend on: `lambda_pos_finite_height` there is\nproved from `SfBoundProp` (the single named analytic hypothesis, D-062\ntriage) + the computational perimeter (Platt\u2013Trudgian `RHUpTo`,\n`LiVerifiedUpTo`) + two elementary base-point evaluations. -/"
}
tool: Edit
input
{
"file_path": "D:\\Python\\Quantum\\research\\lean\\NguyenRH1\\NguyenRH1\\LiSkeleton.lean",
"old_string": "theorem marginTilde_eq_sub (F : \u211d \u2192 \u211d) (n : \u211d) :\n marginTilde F n = sInftyLower n - Bn F n + 1 := by\n simp only [marginTilde, Bn, sInftyLower]\n ring",
"new_string": "theorem marginTilde_eq_sub (F : \u211d \u2192 \u211d) (n : \u211d) :\n marginTilde F n = sInftyLower n - Bn F n + 1 := by\n simp only [marginTilde, Bn, sInftyLower]"
}
raw content_json (database row)
[{"type":"thinking","thinking":"It's `ConvexOn.subset (hf : ConvexOn 𝕜 t f) (hst : s ⊆ t) (hs : Convex 𝕜 s) : ConvexOn 𝕜 s f`. So:\n```\nhave hconv' : ConvexOn ℝ (Set.Ici N₀) f :=\n hconv.subset (Set.Ici_subset_Ici.mpr (le_of_lt hN)) (convex_Ici N₀)\n```\n\nNow apply all fixes:\n\n1. Line ~50-56: docstring → plain comment.\n2. marginTilde_eq_sub: drop ring.\n3. hD2: convert → e/rwa pattern.\n4. Delete bogus h2 block.\n5. pos_of_convex_of_base: rw [heq] → rw [← heq]; hfc restructure; hconv.mono → hconv.subset ... (convex_Ici _).\n6. FAlt_psi_neg: {T} → (T).","signature":""},{"type":"text","text":"It's `ConvexOn.subset` with an explicit convexity argument. Applying all fixes now."},{"type":"tool_use","id":"Edit_60","name":"Edit","input":{"file_path":"D:\\Python\\Quantum\\research\\lean\\NguyenRH1\\NguyenRH1\\LiSkeleton.lean","old_string":"/-- [PROVED session 012, tier (ii) step 1 — assembly modulo the named\nanalytic hypothesis] R-004, the finite-height Li theorem (draft Thm 3.1).\nThe full statement and proof are at the END of this file (§4), after the\nmargin machinery they depend on: `lambda_pos_finite_height` there is\nproved from `SfBoundProp` (the single named analytic hypothesis, D-062\ntriage) + the computational perimeter (Platt–Trudgian `RHUpTo`,\n`LiVerifiedUpTo`) + two elementary base-point evaluations. -/","new_string":"/- [PROVED session 012, tier (ii) step 1 — assembly modulo the named\nanalytic hypothesis] R-004, the finite-height Li theorem (draft Thm 3.1).\nThe full statement and proof are at the END of this file (§4), after the\nmargin machinery they depend on: `lambda_pos_finite_height` there is\nproved from `SfBoundProp` (the single named analytic hypothesis, D-062\ntriage) + the computational perimeter (Platt–Trudgian `RHUpTo`,\n`LiVerifiedUpTo`) + two elementary base-point evaluations. -/"},"extra_content":null},{"type":"tool_use","id":"Edit_61","name":"Edit","input":{"file_path":"D:\\Python\\Quantum\\research\\lean\\NguyenRH1\\NguyenRH1\\LiSkeleton.lean","old_string":"theorem marginTilde_eq_sub (F : ℝ → ℝ) (n : ℝ) :\n marginTilde F n = sInftyLower n - Bn F n + 1 := by\n simp only [marginTilde, Bn, sInftyLower]\n ring","new_string":"theorem marginTilde_eq_sub (F : ℝ → ℝ) (n : ℝ) :\n marginTilde F n = sInftyLower n - Bn F n + 1 := by\n simp only [marginTilde, Bn, sInftyLower]"},"extra_content":null}]