[{"type":"thinking","thinking":"Confirmed: `intervalIntegral.integral_mono_on (hab : a ≤ b) (hf : IntervalIntegrable f μ a b) (hg : IntervalIntegrable g μ a b) (h : ∀ x ∈ Icc a b, f x ≤ g x)`.\n\nNow verify the general lemmas. Let me grep for:\n- `norm_le_insert`\n- `Complex.abs_re_le_norm`\n- `norm_natCast` (for ℂ)\n- `Real.le_log_iff_exp_le`\n- `Real.exp_one_lt_d9`\n- `Real.le_sqrt`\n- `div_eq_mul_one_div`\n- `norm_sum_le`\n- `Finset.mul_sum`\n- `continuous_iff_continuousAt`\n- `ContinuousAt.comp`\n- `Continuous.norm`\n- `IsNontrivialZero` definition (field structure) in Zeta23.","signature":""},{"type":"text","text":"Confirmed. Now verifying the remaining general lemmas and the `IsNontrivialZero` structure."},{"type":"tool_use","id":"Grep_17","name":"Grep","input":{"pattern":"theorem norm_le_insert |theorem abs_re_le_norm |theorem norm_natCast |theorem le_log_iff_exp_le |theorem exp_one_lt_d9|theorem le_sqrt |theorem div_eq_mul_one_div |theorem norm_sum_le |theorem mul_sum |theorem continuous_iff_continuousAt |protected theorem Continuous\\.norm |theorem abs_of_nonneg |theorem abs_of_neg |theorem log_nonneg |theorem one_div_le_one_div_of_le |theorem mul_le_mul_of_nonneg_left |theorem mul_le_mul ","path":"D:\\Python\\Quantum\\zeta-23-lean\\.lake\\packages\\mathlib\\Mathlib","output_mode":"content","-A":2,"head_limit":80},"extra_content":null}]