[{"type":"thinking","thinking":"`Summable.tsum_le_tsum` — used in Zeta23 as `Summable.tsum_le_tsum (fun n => ?_) (summable_proof) (summable_proof)` and `(summable_re_terms ...).tsum_le_tsum hterm` (dot form: hf.tsum_le_tsum h — with hf the FIRST summable). So the signature: `Summable.tsum_le_tsum (h : ∀ i, f i ≤ g i) (hf : Summable f) (hg : Summable g)` — wait the dot-form `(summable_re_terms ha0 ha1 t₁).tsum_le_tsum hterm` — the receiver is the first Summable (f's). So: Summable.tsum_le_tsum (h : ∀ i, f i ≤ g i) (hf : Summable f) (hg : Summable g)?? — with dot-receiver filling hf — but the args order... let me check the exact: from StirlingVert:348: `refine Summable.tsum_le_tsum (fun n => ?_) (summable_norm_rho hw ht) ?_` — so args: (h : ∀ i, f i ≤ g i) then (hf : Summable f) then (hg : Summable g) — two explicit summable args. So the name is `Summable.tsum_le_tsum` (protected, in Summable namespace) with (h) (hf) (hg). My usages: `tsum_le_tsum hterm h1 (...).summable` — should be `Summable.tsum_le_tsum hterm h1 (...)`. Let me fix both occurrences (the htail calc and hser's calc step).","signature":""},{"type":"text","text":"`Summable.tsum_le_tsum` is the name. Fixing the two occurrences plus the div_eq_iff and div_le_div issues."},{"type":"tool_use","id":"Bash_371","name":"Bash","input":{"command":"cd /d/Python/Quantum/research/lean/NguyenRH1/NguyenRH1 && grep -n \"tsum_le_tsum\\|div_eq_iff (by positivity : (0 : ℝ)\" LiDigammaLeft.lean | head -8","description":"Find all tsum_le_tsum and div_eq_iff spots"},"extra_content":null}]