[{"type":"thinking","thinking":"Two errors:\n\n1. Line 105: `rw [hw_def, ← one_div, div_le_one hk1]` — the `← one_div` rewrite failed because after rw [hw_def] the goal has `1 / (2 * (↑k + 1))` and `← one_div` looks for `?a⁻¹` pattern — `1 / x` is `x⁻¹` already in ℝ (division by is mul with inv... `1 / x` is displayed as is but is `1 * x⁻¹`? Hmm — `one_div : 1 / a = a⁻¹`; the goal shows `1 / (2 * (↑k + 1))` which might BE `1 * (2*(↑k+1))⁻¹`... The rewrite `← one_div` wants to turn `x⁻¹` into `1/x`, but the term is already `1 / x` form = `HDiv.hDiv 1 x` — one_div is `1 / a = a⁻¹`, so `← one_div` rewrites `a⁻¹` to `1/a` — there's no `⁻¹` occurrence since it's already `1/a`. So just drop the `← one_div`: after rw [hw_def], directly `rw [div_le_one hk1]`? The goal: `(2 * ↑j + 1) * (1 / (2 * (↑k + 1))) ≤ 1`. div_le_one is about `a / b ≤ 1` — the term is a product with a division, not a division. Fix: rearrange first: `mul_one_div`: a * (1/b) = a/b. So: `rw [hw_def, mul_one_div, div_le_one hk1]; exact hju`? wait after hw_def: `(2*↑j+1) * (1 / (2*(↑k+1))) ≤ 1` → mul_one_div: `(2*↑j+1) / (2*(↑k+1)) ≤ 1` → div_le_one hk1: needs `2*↑j+1 ≤ 2*(↑k+1)` = hju ✓. \n\nHmm — actually simpler: `rw [hw_def]; rw [div_le_iff₀ hk1]`? no. Just: `rw [hw_def, mul_one_div, div_le_one hk1]; exact hju`. Wait — but `w := 1/(2*(↑k+1))` and the hypothesis `h2 : (2 * ↑j + 1) * w ≤ 1` — `rw [hw_def]` rewrites w... h2 is the goal being proved (`have h2 : (2 * ↑j + 1) * w ≤ 1 := by ...`). rw hw_def in goal: `(2*↑j+1) * (1/(2*(↑k+1))) ≤ 1` ✓ then mul_one_div ✓ then div_le_one hk1 turns goal into `2*↑j+1 ≤ 2*(↑k+1)` ✓ exact hju.\n\nHmm wait, does `div_le_one` need `0 < b`: `div_le_one (hb : 0 < b) : a / b ≤ 1 ↔ a ≤ b` ✓ hk1.\n\n2. Line 124: in hinj, the `h3` after rw: `h3 : |c i - c j| ≤ |f j - c i| + |f j - c j|` — the rw [abs_sub_comm (c i) (f i), hij] at h3 turned `|c i - f i|` into `|f i - c i|`?? wait: abs_sub_comm (c i) (f i) : |c i − f i| = |f i − c i| ✓, and hij : f i = f j rewrites f i to f j: h3 : |c i − c j| ≤ |f j − c i| + |f j − c j| ✓ as shown. Then linarith needs: |c i − c j| < 2w from h3, h1 : |f i − c i| < w, h2 : |f j − c j| < w. Note |f j − c i| = |f i − c i| (hij) — but linarith doesn't know |f j − c i| = |f i − c i| since hij was rewritten away... h1 mentions |f i − c i|, h3 mentions |f j − c i| — DIFFERENT terms syntactically! linarith treats them as independent. Fix: rewrite h1 using hij first: `rw [hij] at h1` making h1 : |f j − c i| < w. Then linarith [h1, h2, h3]... but also need nonneg of abs terms? |f j − c i| + |f j − c j| < w + w = 2w ⟹ |c i − c j| < 2w: linear in the abs atoms ✓ linarith handles (abs as atoms, all present).\n\nSo in hlt: \n```lean\nhave hlt : |c i - c j| < 2 * w := by\n  have h3 : |c i - c j| ≤ |c i - f i| + |f i - c j| := abs_sub_le (c i) (f i) (c j)\n  rw [abs_sub_comm (c i) (f i)] at h3  -- |f i − c i|\n  rw [hij] at h1 h3  -- h1 : |f j − c i| < w; h3 : |c i − c j| ≤ |f j − c i| + |f j − c j|\n  linarith [h1, h2, h3]\n```\nWait — careful: rw [hij] at h3 — h3 contains f i once (after abs_sub_comm): becomes f j ✓. h1 : |f i − c i| < w → rw hij → |f j − c i| < w ✓. Then linarith [h1, h2, h3]: h3: |ci−cj| ≤ |fj−ci| + |fj−cj|, h1: |fj−ci| < w, h2: |fj−cj| < w ⟹ |ci−cj| < 2w ✓ linear.\n\nHmm — but `hij : f i = f j` — rw [hij] at h1 rewrites occurrences of `f i` in h1 ✓.\n\nAlso the error message shows hlt's proof ended with `linarith` failing with `a✝ : 2 * w ≤ |c i - c j|` — wait that's the second part? The error at 124:6 is inside... line 124 is `linarith` in hlt. Yes fix as above.\n\nThen `have hge : 2 * w ≤ |2 * ((i:ℝ) - j) * w|` and final `linarith` — with hlt and hge: linarith should close False ✓ (hge + hlt: 2w ≤ |...| < 2w ⟹ False).\n\nWait — after fixing hlt, the final linarith [hlt, hge]? I wrote just `linarith` — it uses context: hlt, hge both in context ✓.\n\nAlso the push_neg deprecation warning — replace with `push Not at hcon`? The warning says prefer `push Not`. Let me use that to keep the build warning-clean. Hmm — is `push Not at hcon` valid syntax in this Mathlib version? The deprecation suggests `push $cfg:optConfig Not` — so `push Not at hcon` ✓.\n\nAlso there was another warning at 171 \"Try this:\" — truncated output. Let me fix the two errors + push_neg, then rerun to see remaining issues.","signature":""},{"type":"text","text":"Two errors: the `← one_div` rewrite (already in `1/x` form) and a syntactic mismatch after rewriting `hij` (need to rewrite `h1` too). Fixing both plus the `push_neg` deprecation."},{"type":"tool_use","id":"Edit_64","name":"Edit","input":{"replace_all":false,"file_path":"D:\\Python\\Quantum\\research\\lean\\NguyenRH1\\NguyenRH1\\LiContour.lean","old_string":"    have h2 : (2 * (j : ℝ) + 1) * w ≤ 1 := by\n      rw [hw_def, ← one_div, div_le_one hk1]\n      exact hju","new_string":"    have h2 : (2 * (j : ℝ) + 1) * w ≤ 1 := by\n      rw [hw_def, mul_one_div, div_le_one hk1]\n      exact hju"},"extra_content":null}]