← Session 31 — ii′-5f: tight R-bound 10.5/48 (piece 3 + pinch)
thinking (1944 chars)
The whnf timeout at 3677:5 is at the hle line: `Summable.tsum_le_tsum (fun k => farGRightMaj_le_combo ht (k + 11)) (farGRightMaj_summable ht) farGRightMajCombo_shift_summable` — Summable.tsum_le_tsum (h : ∀ i, f i ≤ g i) (hf : Summable f L) (hg : Summable g L) : ∑'[L] f ≤ ∑'[L] g — the FUNCTIONS f,g must be inferred from the proofs: hf := farGRightMaj_summable ht : Summable (farGRightMaj t) — f := farGRightMaj t ✓; hg := farGRightMajCombo_shift_summable : Summable (fun k => farGRightMajCombo (k+11)) — g := fun k => farGRightMajCombo (k+11) ✓. The h : ∀ i, f i ≤ g i := fun k => farGRightMaj_le_combo ht (k+11) : ∀ k, farGRightMaj t (k+11) ≤ farGRightMajCombo (k+11) ✓ — f := fun k => farGRightMaj t (k+11)!! — MISMATCH: hf's f is farGRightMaj t (unshifted!), but h's f is fun k => farGRightMaj t (k+11)!!
THE BUG: hle compares tsum(farGRightMaj t (k+11)) with tsum(farGRightMajCombo (k+11)) — but farGRightMaj_summable ht : Summable (farGRightMaj t) — the UNSHIFTED. Summable.tsum_le_tsum needs hf : Summable f with f = the SHIFTED family fun k => farGRightMaj t (k+11). So I need hf := the shifted summable: (summable_nat_add_iff 11).mpr (farGRightMaj_summable ht) : Summable (fun k => farGRightMaj t (k+11)).
The whnf timeout is the elaborator trying to unify the mismatched f's. Fix:
```
have hle := Summable.tsum_le_tsum (fun k => farGRightMaj_le_combo ht (k + 11))
((summable_nat_add_iff (f := farGRightMaj t) 11).mpr (farGRightMaj_summable ht))
farGRightMajCombo_shift_summable
```
Same pattern as §17's hle — wait, §17's hle used `farGLeftMaj_shift_summable` (the standalone shifted one) ✓ — I need the analogous farGRightMaj_shift_summable standalone or the inline .mpr. Let me add a standalone:
```
lemma farGRightMaj_shift_summable {t : ℝ} (ht : 10 ≤ t) :
Summable (fun k : ℕ => farGRightMaj t (k + 11)) :=
(summable_nat_add_iff (f := farGRightMaj t) 11).mpr (farGRightMaj_summable ht)
```
and use it in hle.
Found it — the shifted/unshifted summable mismatch in hle. Fixing.
tool: Bash
input
{
"command": "cd D:/Python/Quantum/research/lean/NguyenRH1 && python - <<'EOF'\np = 'NguyenRH1/LiTightR.lean'\nsrc = open(p, encoding='utf-8').read()\n\nold = \"\"\"/-- **The right-tail series bound**. -/\"\"\"\nnew = \"\"\"lemma farGRightMaj_shift_summable {t : \u211d} (ht : 10 \u2264 t) :\n Summable (fun k : \u2115 => farGRightMaj t (k + 11)) :=\n (summable_nat_add_iff (f := farGRightMaj t) 11).mpr (farGRightMaj_summable ht)\n\n/-- **The right-tail series bound**. -/\"\"\"\nassert old in src\nsrc = src.replace(old, new, 1)\n\nold2 = \"\"\" have hle := Summable.tsum_le_tsum (fun k => farGRightMaj_le_combo ht (k + 11))\n (farGRightMaj_summable ht) farGRightMajCombo_shift_summable\"\"\"\nnew2 = \"\"\" have hle := Summable.tsum_le_tsum (fun k => farGRightMaj_le_combo ht (k + 11))\n (farGRightMaj_shift_summable ht) farGRightMajCombo_shift_summable\"\"\"\nassert old2 in src\nsrc = src.replace(old2, new2)\nopen(p, 'w', encoding='utf-8').write(src)\nprint(\"done\")\nEOF\nexport PATH=\"$HOME/.elan/bin:$PATH\" && lake env lean NguyenRH1/LiTightR.lean 2>&1 | head -20",
"description": "Add shifted summable and fix hle, recompile",
"timeout": 420000
}
raw content_json (database row)
[{"type":"thinking","thinking":"The whnf timeout at 3677:5 is at the hle line: `Summable.tsum_le_tsum (fun k => farGRightMaj_le_combo ht (k + 11)) (farGRightMaj_summable ht) farGRightMajCombo_shift_summable` — Summable.tsum_le_tsum (h : ∀ i, f i ≤ g i) (hf : Summable f L) (hg : Summable g L) : ∑'[L] f ≤ ∑'[L] g — the FUNCTIONS f,g must be inferred from the proofs: hf := farGRightMaj_summable ht : Summable (farGRightMaj t) — f := farGRightMaj t ✓; hg := farGRightMajCombo_shift_summable : Summable (fun k => farGRightMajCombo (k+11)) — g := fun k => farGRightMajCombo (k+11) ✓. The h : ∀ i, f i ≤ g i := fun k => farGRightMaj_le_combo ht (k+11) : ∀ k, farGRightMaj t (k+11) ≤ farGRightMajCombo (k+11) ✓ — f := fun k => farGRightMaj t (k+11)!! — MISMATCH: hf's f is farGRightMaj t (unshifted!), but h's f is fun k => farGRightMaj t (k+11)!! \n\nTHE BUG: hle compares tsum(farGRightMaj t (k+11)) with tsum(farGRightMajCombo (k+11)) — but farGRightMaj_summable ht : Summable (farGRightMaj t) — the UNSHIFTED. Summable.tsum_le_tsum needs hf : Summable f with f = the SHIFTED family fun k => farGRightMaj t (k+11). So I need hf := the shifted summable: (summable_nat_add_iff 11).mpr (farGRightMaj_summable ht) : Summable (fun k => farGRightMaj t (k+11)). \n\nThe whnf timeout is the elaborator trying to unify the mismatched f's. Fix:\n```\n have hle := Summable.tsum_le_tsum (fun k => farGRightMaj_le_combo ht (k + 11))\n ((summable_nat_add_iff (f := farGRightMaj t) 11).mpr (farGRightMaj_summable ht))\n farGRightMajCombo_shift_summable\n```\nSame pattern as §17's hle — wait, §17's hle used `farGLeftMaj_shift_summable` (the standalone shifted one) ✓ — I need the analogous farGRightMaj_shift_summable standalone or the inline .mpr. Let me add a standalone:\n```\nlemma farGRightMaj_shift_summable {t : ℝ} (ht : 10 ≤ t) :\n Summable (fun k : ℕ => farGRightMaj t (k + 11)) :=\n (summable_nat_add_iff (f := farGRightMaj t) 11).mpr (farGRightMaj_summable ht)\n```\nand use it in hle.","signature":""},{"type":"text","text":"Found it — the shifted/unshifted summable mismatch in hle. Fixing."},{"type":"tool_use","id":"Bash_248","name":"Bash","input":{"command":"cd D:/Python/Quantum/research/lean/NguyenRH1 && python - <<'EOF'\np = 'NguyenRH1/LiTightR.lean'\nsrc = open(p, encoding='utf-8').read()\n\nold = \"\"\"/-- **The right-tail series bound**. -/\"\"\"\nnew = \"\"\"lemma farGRightMaj_shift_summable {t : ℝ} (ht : 10 ≤ t) :\n Summable (fun k : ℕ => farGRightMaj t (k + 11)) :=\n (summable_nat_add_iff (f := farGRightMaj t) 11).mpr (farGRightMaj_summable ht)\n\n/-- **The right-tail series bound**. -/\"\"\"\nassert old in src\nsrc = src.replace(old, new, 1)\n\nold2 = \"\"\" have hle := Summable.tsum_le_tsum (fun k => farGRightMaj_le_combo ht (k + 11))\n (farGRightMaj_summable ht) farGRightMajCombo_shift_summable\"\"\"\nnew2 = \"\"\" have hle := Summable.tsum_le_tsum (fun k => farGRightMaj_le_combo ht (k + 11))\n (farGRightMaj_shift_summable ht) farGRightMajCombo_shift_summable\"\"\"\nassert old2 in src\nsrc = src.replace(old2, new2)\nopen(p, 'w', encoding='utf-8').write(src)\nprint(\"done\")\nEOF\nexport PATH=\"$HOME/.elan/bin:$PATH\" && lake env lean NguyenRH1/LiTightR.lean 2>&1 | head -20","description":"Add shifted summable and fix hle, recompile","timeout":420000},"extra_content":null}]