← Session 14 — Phase 5 kickoff: paper draft + honesty audit
thinking (398 chars)
`Summable.sum_le_tsum : Summable f → (∀ i ∉ s, 0 ≤ f i) → ∑ i in s, f i ≤ ∑' i, f i` — method form on Summable ✓ (usage: `hf.sum_le_tsum s (fun i _ => zero_le)`).
All the pieces exist. Now — before writing the proof files, start with the warm-up: chain_rule_sqrt_shift. Let me check deriv lemma names: `Real.hasDerivAt_sqrt`, `deriv.comp`, `deriv_mul`, `deriv_const`, `deriv_inv`... Check quickly.
All pieces exist (`Summable.sum_le_tsum` method form). Checking deriv lemma names for the warm-up proof.
tool: Bash
input
{
"command": "cd /d/Python/Quantum/zeta-23-lean/.lake/packages/mathlib && grep -rn \"theorem hasDerivAt_sqrt\\|lemma hasDerivAt_sqrt\" Mathlib/Analysis/SpecialFunctions/Sqrt.lean Mathlib/Analysis/SpecialFunctions/Pow/*.lean 2>/dev/null | head -3; grep -rn \"theorem deriv_sqrt\\|lemma deriv_sqrt\" Mathlib/Analysis/SpecialFunctions/ 2>/dev/null | head -3; grep -rn \"theorem deriv_mul \\|lemma deriv_mul \" Mathlib/Analysis/Calculus/Deriv/Mul.lean | head -2; grep -rn \"theorem deriv_comp'\\|lemma deriv.comp\\b\" Mathlib/Analysis/Calculus/Deriv/Comp.lean | head -4",
"description": "Check deriv lemma names"
}
raw content_json (database row)
[{"type":"thinking","thinking":"`Summable.sum_le_tsum : Summable f → (∀ i ∉ s, 0 ≤ f i) → ∑ i in s, f i ≤ ∑' i, f i` — method form on Summable ✓ (usage: `hf.sum_le_tsum s (fun i _ => zero_le)`).\n\nAll the pieces exist. Now — before writing the proof files, start with the warm-up: chain_rule_sqrt_shift. Let me check deriv lemma names: `Real.hasDerivAt_sqrt`, `deriv.comp`, `deriv_mul`, `deriv_const`, `deriv_inv`... Check quickly.","signature":""},{"type":"text","text":"All pieces exist (`Summable.sum_le_tsum` method form). Checking deriv lemma names for the warm-up proof."},{"type":"tool_use","id":"Bash_158","name":"Bash","input":{"command":"cd /d/Python/Quantum/zeta-23-lean/.lake/packages/mathlib && grep -rn \"theorem hasDerivAt_sqrt\\|lemma hasDerivAt_sqrt\" Mathlib/Analysis/SpecialFunctions/Sqrt.lean Mathlib/Analysis/SpecialFunctions/Pow/*.lean 2>/dev/null | head -3; grep -rn \"theorem deriv_sqrt\\|lemma deriv_sqrt\" Mathlib/Analysis/SpecialFunctions/ 2>/dev/null | head -3; grep -rn \"theorem deriv_mul \\|lemma deriv_mul \" Mathlib/Analysis/Calculus/Deriv/Mul.lean | head -2; grep -rn \"theorem deriv_comp'\\|lemma deriv.comp\\b\" Mathlib/Analysis/Calculus/Deriv/Comp.lean | head -4","description":"Check deriv lemma names"},"extra_content":null}]