← Session 18 — Lean tier (ii): finite-height proof + certified base points
thinking (498 chars)
- `Real.sqrt_le_left (hy : 0 ≤ y) : √x ≤ y ↔ x ≤ y ^ 2` ✓ (for √80000 ≤ 283)
- `Real.le_sqrt (hx : 0 ≤ x) (hy : 0 ≤ y) : x ≤ √y ↔ x ^ 2 ≤ y` ✓ (for 282 ≤ √80000)
- `Real.pi_gt_d20 : 3.14159265358979323846 < π`, `Real.pi_lt_d20 : π < 3.14159265358979323847` ✓ (d20, even better)
- `Real.exp_nat_mul (x : ℝ) (n : ℕ) : exp (↑n * x) = exp x ^ n` ✓
- `Real.add_one_le_exp (x : ℝ) : x + 1 ≤ Real.exp x` ✓
Now, file organization: new file `NguyenRH1/LiBasePoints.lean`. Check the lib root NguyenRH1.lean:
All names confirmed. Setting up the new file for the numeric discharge.
tool: Read
input
{
"file_path": "D:\\Python\\Quantum\\research\\lean\\NguyenRH1\\NguyenRH1.lean"
}
raw content_json (database row)
[{"type":"thinking","thinking":"- `Real.sqrt_le_left (hy : 0 ≤ y) : √x ≤ y ↔ x ≤ y ^ 2` ✓ (for √80000 ≤ 283)\n- `Real.le_sqrt (hx : 0 ≤ x) (hy : 0 ≤ y) : x ≤ √y ↔ x ^ 2 ≤ y` ✓ (for 282 ≤ √80000)\n- `Real.pi_gt_d20 : 3.14159265358979323846 < π`, `Real.pi_lt_d20 : π < 3.14159265358979323847` ✓ (d20, even better)\n- `Real.exp_nat_mul (x : ℝ) (n : ℕ) : exp (↑n * x) = exp x ^ n` ✓\n- `Real.add_one_le_exp (x : ℝ) : x + 1 ≤ Real.exp x` ✓\n\nNow, file organization: new file `NguyenRH1/LiBasePoints.lean`. Check the lib root NguyenRH1.lean:","signature":""},{"type":"text","text":"All names confirmed. Setting up the new file for the numeric discharge."},{"type":"tool_use","id":"Read_134","name":"Read","input":{"file_path":"D:\\Python\\Quantum\\research\\lean\\NguyenRH1\\NguyenRH1.lean"},"extra_content":null}]