[{"type":"thinking","thinking":"Five errors:\n\n1. **620**: `neg_abs_le (σ - β)` has type `-|σ - β| ≤ σ - β` — I had it backwards: `neg_abs_le : -|a| ≤ a`. I need `-(σ−β) ≤ |σ−β|` — that's `neg_le_abs (a) : -a ≤ |a|`? Hmm — `neg_le_abs_self`? In Mathlib: `neg_le_abs (a) : -a ≤ |a|` ✓ I believe `neg_le_abs` exists. Let me use `neg_le_abs`.\n\n2. **629/631**: `hasDerivAt_id.sub_const` — Unknown constant. hasDerivAt_id is `theorem hasDerivAt_id (x : 𝕜) : HasDerivAt id 1 x`. The dot `.sub_const` on it — `HasDerivAt.sub_const` exists? The error is \"Unknown constant hasDerivAt_id.sub_const\" — because hasDerivAt_id is a FUNCTION (explicit arg x), dot-notation resolution fails?? — `(hasDerivAt_id σ).sub_const β` should work... unless `HasDerivAt.sub_const` doesn't exist under that name. Let me check: in Mathlib, `HasDerivAt.sub_const (hf : HasDerivAt f f' x) (c : 𝕜) : HasDerivAt (fun x => f x - c) f' x` — hmm — maybe it's `HasDerivAt.sub_const` vs the session-011 gotcha: \"HasDerivAt.add_const adds to VALUE (use .comp for precomposition)\" — implying HasDerivAt.add_const EXISTS. So sub_const should too. The error \"Unknown constant `hasDerivAt_id.sub_const`\" — the dot-notation on a FUNCTION (hasDerivAt_id takes explicit x) — `(hasDerivAt_id σ).sub_const β` — Lean parses `hasDerivAt_id.sub_const` as a CONSTANT name first — since hasDerivAt_id is a function needing an argument, the parser treats `.sub_const` as namespace resolution and fails! When the head is a function application, must parenthesize: `(hasDerivAt_id σ).sub_const β` — I DID parenthesize in h2a but NOT in h1: `hasDerivAt_id.sub_const β` (line 629, no parens around hasDerivAt_id σ!). Indeed my h1: `hasDerivAt_id.sub_const β` — WRONG — should be `(hasDerivAt_id σ).sub_const β`. And h2a: `(hasDerivAt_id.sub_const β).pow 2` — also unparenthesized — should be `((hasDerivAt_id σ).sub_const β).pow 2`.\n\n3. **650**: \"No goals to be solved\" — the h6/h7 convert's field_simp; ring — field_simp closed it, ring has no goals. Line 650 — which one? The h7 block ends around 648-650. Let me count: h6 block: convert h5 using 1; field_simp [hsqrt0]; ring — lines ~640-643. h7: have h7 := h6.log hg0; convert h7 using 1; field_simp [hsqrt0, hg0]; ring — ~645-650. Line 650:4 = the `ring` after h7's field_simp — field_simp closed, ring fails. Remove that ring. But wait — did h6's field_simp; ring pass (no error at ~643)? The error list shows only 650 — so h6's ring was FINE (field_simp left a goal there) and h7's field_simp closed fully. Remove the ring after h7's field_simp.\n\n4. **701**: hrid's `rw [div_eq_iff ...]` — \"Did not find the pattern ?a / (u + √) = ?c in the target\". The goal: `-u + √(u^2+δ^2) = δ^2 / (u + √(u^2+δ^2))`. div_eq_iff (hb : b ≠ 0) : a / b = c ↔ a = c * b — the PATTERN for rw [div_eq_iff h] is `?a / ?b = ?c` — i.e., it rewrites goals where the DIVISION is on the LHS! My goal has the division on the RHS: `-u + √ = δ²/(u+√)`. So rw [div_eq_iff] finds no `?/?b = ?c` with b := u+√... wait — the pattern `?m.660 / (u + √(u ^ 2 + δ ^ 2)) = ?m.662` — it needs LHS-of-eq to be a division by (u+√). My goal: `-u+√ = δ²/(u+√)` — the division is the RHS — no match. FIX: rw [eq_div_iff (hb : b ≠ 0) : c = a / b ↔ c * b = a]! `eq_div_iff (hb : 0 < b)`? — `eq_div_iff (hb : b ≠ 0) : c = a / b ↔ c * b = a` ✓ exists. Use `rw [eq_div_iff (ne_of_gt ...)]` — goal becomes `(−u+√)·(u+√) = δ²` — nlinarith [hs] ✓.\n\n5. **793**: hB0nn's `nlinarith [hC0]` failed: goal `1 ≤ 148.5 * C0hat(√n+2)` with hC0 : 0 < C0hat — I need C0hat ≥ 2 (two_le_C0hat), not just > 0! I wrote `nlinarith [hC0]` but hC0 is only 0 < C0hat. The hB0nn block references hC0 but the needed fact is h2 := two_le_C0hat (which I computed INSIDE the hC0 block — not in scope here!). Fix: in hB0nn, use two_le_C0hat directly:\n```lean\n  have hB0nn : (0 : ℝ) ≤ 2 * Real.log (148.5 * C0hat (Real.sqrt (n : ℝ) + 2)) := by\n    have h2 := two_le_C0hat (by nlinarith [Real.sqrt_nonneg (n : ℝ)] :\n      (1 : ℝ) ≤ Real.sqrt (n : ℝ) + 2)\n    have h1 : (1 : ℝ) ≤ 148.5 * C0hat (Real.sqrt (n : ℝ) + 2) := by nlinarith [h2]\n    have h3 := Real.log_nonneg h1\n    linarith\n```\n\n6. **777:60 \"unsolved goals\"** — case h — the hne1 block! `intro σ h; have him := congrArg Complex.im h; simp at him; linarith [h10T]` — the context shows hne1 : ∀ σ, ↑σ + ↑T * I ≠ 1 got PROVED (it's in context at 777) — wait no, 777's context ends at hcontJ — the error is at 777:60 — let me find what's at line 777. The error context includes hB0nn, hzne, hne1, hpath, hLDc, hJcont, hcontJ — so 777 is AFTER hcontJ — it's the hcontG/hJintbl region?? Line 777:60 \"unsolved goals case h\" — hmm — col 60. Could be hcontJ's exact line? No — hcontJ is in context (proved). The next block: hcontG := continuous_norm.comp hcontJ — that's an exact-term, no goals. hJintbl := hcontG.intervalIntegrable _ _ — also term. Hmm — \"case h\" — a named case from rcases/obtain/intro... Let me look at line 777.\n\nActually — the errors after 701 are probably CASCADES — 701's failure left hrid sorry'd, but that's in arcsinh_left_endpoint_le (lemma 3) — the subsequent hden/hge/hlog in that lemma would still elaborate (hlogid uses hrid? no — hlogid is independent; hge uses hrid — sorry-backed, fine). The 793 error is independent (hB0nn). The 777 error — let me count lines precisely. I'll read the file around 770-800.","signature":""},{"type":"text","text":"Five fixes identified. Checking the exact line 777 context before fixing."},{"type":"tool_use","id":"Read_98","name":"Read","input":{"file_path":"D:\\Python\\Quantum\\research\\lean\\NguyenRH1\\NguyenRH1\\LiSideBounds.lean","offset":770,"limit":30},"extra_content":null}]