← Session 18 — Lean tier (ii): finite-height proof + certified base points
thinking (964 chars)
Wait — I have a bug in hlogT2's hbig: I wrote a nonsense chain `(le_trans (by norm_num : (286 : ℝ) ≤ 284) h57big ▸ ...)` — 286 ≤ 284 is FALSE. Let me fix: T8+2 ≤ 286 and 286 ≤ exp 5.7 ⟸ 286 ≤ 284? NO — 286 > 284. The chain should be: T8+2 ≤ 286 ≤ 298.674 ≤ exp 5.7. My h57big : 284 ≤ exp 5.7 — so 286 ≤ exp 5.7 by le_trans (286 ≤ 298.674... hmm h57big says 284 ≤ exp 5.7; 286 ≤ exp 5.7 needs 286 ≤ (the certified 298.674) or directly le_trans (286 ≤ 284?? no. Fix: make a separate bound: (286 : ℝ) ≤ Real.exp 5.7 := le_trans (by norm_num : 286 ≤ 298.674...) hmm — h57big's proof gives 284 ≤ 148.328·2.0136 ≤ exp 5.7. For 286: 286 ≤ 148.328·2.0136 = 298.674 ✓ norm_num. So:
```
have h57big2 : (286 : ℝ) ≤ Real.exp 5.7 := by
rw [h57]
exact le_trans (by norm_num : (286 : ℝ) ≤ 148.328 * 2.0136)
(mul_le_mul h5 h07 (by norm_num) (Real.exp_pos _).le)
```
Then hbig : T8+2 ≤ exp 5.7 := le_trans (by linarith : T8+2 ≤ 286) h57big2.
Let me fix that block.
I introduced a broken chain in `hlogT2` (286 ≤ 284 is false). Fixing with a proper 286-bound.
tool: Edit
input
{
"file_path": "D:\\Python\\Quantum\\research\\lean\\NguyenRH1\\NguyenRH1\\LiBasePoints.lean",
"old_string": " have hlogT2 : Real.log (Real.sqrt 80000 + 1 + 2) \u2264 (5.7 : \u211d) := by\n have hbig : Real.sqrt 80000 + 1 + 2 \u2264 Real.exp 5.7 := by\n have h : Real.sqrt 80000 + 1 + 2 \u2264 (286 : \u211d) := by linarith\n exact le_trans h (le_trans (by norm_num : (286 : \u211d) \u2264 284) h57big \u25b8\n (by linarith [h57big]))\n have hT2pos : (0 : \u211d) < Real.sqrt 80000 + 1 + 2 := by linarith\n have h := Real.log_le_log hT2pos hbig\n rwa [Real.log_exp] at h",
"new_string": " have h57big2 : (286 : \u211d) \u2264 Real.exp 5.7 := by\n rw [h57]\n exact le_trans (by norm_num : (286 : \u211d) \u2264 148.328 * 2.0136)\n (mul_le_mul h5 h07 (by norm_num) (Real.exp_pos _).le)\n have hlogT2 : Real.log (Real.sqrt 80000 + 1 + 2) \u2264 (5.7 : \u211d) := by\n have hbig : Real.sqrt 80000 + 1 + 2 \u2264 Real.exp 5.7 := by\n have h : Real.sqrt 80000 + 1 + 2 \u2264 (286 : \u211d) := by linarith\n exact le_trans h h57big2\n have hT2pos : (0 : \u211d) < Real.sqrt 80000 + 1 + 2 := by linarith\n have h := Real.log_le_log hT2pos hbig\n rwa [Real.log_exp] at h"
}
raw content_json (database row)
[{"type":"thinking","thinking":"Wait — I have a bug in hlogT2's hbig: I wrote a nonsense chain `(le_trans (by norm_num : (286 : ℝ) ≤ 284) h57big ▸ ...)` — 286 ≤ 284 is FALSE. Let me fix: T8+2 ≤ 286 and 286 ≤ exp 5.7 ⟸ 286 ≤ 284? NO — 286 > 284. The chain should be: T8+2 ≤ 286 ≤ 298.674 ≤ exp 5.7. My h57big : 284 ≤ exp 5.7 — so 286 ≤ exp 5.7 by le_trans (286 ≤ 298.674... hmm h57big says 284 ≤ exp 5.7; 286 ≤ exp 5.7 needs 286 ≤ (the certified 298.674) or directly le_trans (286 ≤ 284?? no. Fix: make a separate bound: (286 : ℝ) ≤ Real.exp 5.7 := le_trans (by norm_num : 286 ≤ 298.674...) hmm — h57big's proof gives 284 ≤ 148.328·2.0136 ≤ exp 5.7. For 286: 286 ≤ 148.328·2.0136 = 298.674 ✓ norm_num. So:\n```\n have h57big2 : (286 : ℝ) ≤ Real.exp 5.7 := by\n rw [h57]\n exact le_trans (by norm_num : (286 : ℝ) ≤ 148.328 * 2.0136)\n (mul_le_mul h5 h07 (by norm_num) (Real.exp_pos _).le)\n```\nThen hbig : T8+2 ≤ exp 5.7 := le_trans (by linarith : T8+2 ≤ 286) h57big2.\n\nLet me fix that block.","signature":""},{"type":"text","text":"I introduced a broken chain in `hlogT2` (286 ≤ 284 is false). Fixing with a proper 286-bound."},{"type":"tool_use","id":"Edit_154","name":"Edit","input":{"file_path":"D:\\Python\\Quantum\\research\\lean\\NguyenRH1\\NguyenRH1\\LiBasePoints.lean","old_string":" have hlogT2 : Real.log (Real.sqrt 80000 + 1 + 2) ≤ (5.7 : ℝ) := by\n have hbig : Real.sqrt 80000 + 1 + 2 ≤ Real.exp 5.7 := by\n have h : Real.sqrt 80000 + 1 + 2 ≤ (286 : ℝ) := by linarith\n exact le_trans h (le_trans (by norm_num : (286 : ℝ) ≤ 284) h57big ▸\n (by linarith [h57big]))\n have hT2pos : (0 : ℝ) < Real.sqrt 80000 + 1 + 2 := by linarith\n have h := Real.log_le_log hT2pos hbig\n rwa [Real.log_exp] at h","new_string":" have h57big2 : (286 : ℝ) ≤ Real.exp 5.7 := by\n rw [h57]\n exact le_trans (by norm_num : (286 : ℝ) ≤ 148.328 * 2.0136)\n (mul_le_mul h5 h07 (by norm_num) (Real.exp_pos _).le)\n have hlogT2 : Real.log (Real.sqrt 80000 + 1 + 2) ≤ (5.7 : ℝ) := by\n have hbig : Real.sqrt 80000 + 1 + 2 ≤ Real.exp 5.7 := by\n have h : Real.sqrt 80000 + 1 + 2 ≤ (286 : ℝ) := by linarith\n exact le_trans h h57big2\n have hT2pos : (0 : ℝ) < Real.sqrt 80000 + 1 + 2 := by linarith\n have h := Real.log_le_log hT2pos hbig\n rwa [Real.log_exp] at h"},"extra_content":null}]