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← Session 28 — ii′-5e: partial-fraction identity (zero series + F entire)

#1539 assistant 2026-08-23 17:41:52.349 UTC · 1889→1129 tok open ⤢
thinking (3490 chars)
The structure looks fine. The error "150:4 unknown identifier linarith" + "150:35 unexpected token '/--' expected :=" — hmm col 35 of line 150 is beyond the line length (line 150 is ` linarith [ih, hwin, hle1, hle2]` — 35 chars: position near the end). The parser is treating line 150's `linarith` as an unknown identifier — that means the TACTIC BLOCK of the succ case ended before line 150 — i.e., the parser thinks the case is done. Why? The `by` blocks with `calc` inside... hle1's proof: `:= by have h2 := ...; calc ...` — wait — hle1's by-block contains a `calc` whose steps are `≤ ... := by ...` — nested by-blocks inside a calc inside a case — indentation-sensitive! hle1's calc block: ``` calc A0count * ... ≤ A0count * ((N:ℝ)+1) * ... := by have hA0 := ... ... exact h4.trans h5 ``` The calc continuation lines at indent 10, the `:= by` at 10, the inner tactics at 12 — the calc's first line at indent 6 (` calc`), continuation `≤ ... := by` at 10, inner at 12, `exact` at 12. For the calc to parse, the continuation lines must be MORE indented than `calc` (6) ✓ 10 > 6 ✓. Then hle2 at indent 4 ✓. Then line 150 `linarith [...]` at indent 4 ✓ should be part of the succ case... Hmm wait — the error at 150:4 "unknown identifier linarith" AND "150:35 unexpected token '/--'; expected ':='". Line 150's content is 33 chars; col 35 is beyond — these error positions look like they belong to the OLD file version (before my edits). The compile might have used a STALE... no. OR — the REAL parse problem: line 150 `linarith [ih, hwin, hle1, hle2]` — if the succ-case by-block got terminated early (e.g. the hle2 block's `linarith` at line 149 completed hle2 AND the parser then saw `linarith` at 150 as the start of a NEW command — because the `| succ N ih =>` case body was... no wait — the case body is a tactic sequence; after hle2's by closes at 149, line 150 IS the next tactic of the case ✓ should parse... UNLESS — the `induction N with | zero => ... | succ N ih => ...` — and my zero-case ended at line 103 `simp` — and the `| succ N ih =>` at 104 — with the case bodies as tactic sequences — when a case's sequence contains a `have ... := by` whose own by-block contains... I bet the problem is the `calc` inside hle1 with a `:= by` whose inner block's LAST line `exact h4.trans h5` is at indent 12 — and the following `have hle2` at indent 4 — calc block ends ✓... Actually — WAIT. I see it now! Line 145-146: ``` apply mul_le_mul_of_nonneg_left _ A0count_pos.le apply Real.log_le_log (by positivity) ``` If `apply Real.log_le_log (by positivity)` left TWO goals (the x ≤ y AND something), then `have h1 ...` at line 147 begins a NEW have while goals remain — that's fine syntactically (have adds to the context of the first goal)... then `linarith` at 149 closes goal 1 but goal 2 remains → "unsolved goals" not parse error. Hmm, let me look at the error list again: "150:35: unexpected token '/--'; expected ':='". Col 35 — line 150 is only 33 chars. So the error position is NOT line 150 of the current file — the compiler's line numbering... could the error be at line 150 counting differently? Line 152 is the /-- doc comment. "unexpected token '/--'" — the token IS the doc comment at 152. Its column: the doc comment starts at col 0... "150:35" though. Ugh. Let me try a completely different diagnostic: run lean with more context — get the FULL error output unfiltered for the parse error.
Let me see the full unfiltered error context around the parse failure.
tool: Bash
input
{
  "command": "export PATH=\"$HOME/.elan/bin:$PATH\" && cd D:/Python/Quantum/research/lean/NguyenRH1 && lake env lean NguyenRH1/LiCircleBound.lean 2>&1 | grep -B3 -A12 \"unexpected token\" | head -30",
  "description": "Full parse error context",
  "timeout": 300000
}
raw content_json (database row)
[{"type":"thinking","thinking":"The structure looks fine. The error \"150:4 unknown identifier linarith\" + \"150:35 unexpected token '/--' expected :=\" — hmm col 35 of line 150 is beyond the line length (line 150 is `    linarith [ih, hwin, hle1, hle2]` — 35 chars: position near the end). The parser is treating line 150's `linarith` as an unknown identifier — that means the TACTIC BLOCK of the succ case ended before line 150 — i.e., the parser thinks the case is done. Why? The `by` blocks with `calc` inside... hle1's proof: `:= by have h2 := ...; calc ...` — wait — hle1's by-block contains a `calc` whose steps are `≤ ... := by ...` — nested by-blocks inside a calc inside a case — indentation-sensitive! hle1's calc block:\n```\n      calc A0count * ... \n          ≤ A0count * ((N:ℝ)+1) * ... := by\n            have hA0 := ...\n            ...\n            exact h4.trans h5\n```\nThe calc continuation lines at indent 10, the `:= by` at 10, the inner tactics at 12 — the calc's first line at indent 6 (`      calc`), continuation `≤ ... := by` at 10, inner at 12, `exact` at 12. For the calc to parse, the continuation lines must be MORE indented than `calc` (6) ✓ 10 > 6 ✓. Then hle2 at indent 4 ✓. Then line 150 `linarith [...]` at indent 4 ✓ should be part of the succ case...\n\nHmm wait — the error at 150:4 \"unknown identifier linarith\" AND \"150:35 unexpected token '/--'; expected ':='\". Line 150's content is 33 chars; col 35 is beyond — these error positions look like they belong to the OLD file version (before my edits). The compile might have used a STALE... no. OR — the REAL parse problem: line 150 `linarith [ih, hwin, hle1, hle2]` — if the succ-case by-block got terminated early (e.g. the hle2 block's `linarith` at line 149 completed hle2 AND the parser then saw `linarith` at 150 as the start of a NEW command — because the `| succ N ih =>` case body was... no wait — the case body is a tactic sequence; after hle2's by closes at 149, line 150 IS the next tactic of the case ✓ should parse...\n\nUNLESS — the `induction N with | zero => ... | succ N ih => ...` — and my zero-case ended at line 103 `simp` — and the `| succ N ih =>` at 104 — with the case bodies as tactic sequences — when a case's sequence contains a `have ... := by` whose own by-block contains... I bet the problem is the `calc` inside hle1 with a `:= by` whose inner block's LAST line `exact h4.trans h5` is at indent 12 — and the following `have hle2` at indent 4 — calc block ends ✓...\n\nActually — WAIT. I see it now! Line 145-146:\n```\n      apply mul_le_mul_of_nonneg_left _ A0count_pos.le\n      apply Real.log_le_log (by positivity)\n```\nIf `apply Real.log_le_log (by positivity)` left TWO goals (the x ≤ y AND something), then `have h1 ...` at line 147 begins a NEW have while goals remain — that's fine syntactically (have adds to the context of the first goal)... then `linarith` at 149 closes goal 1 but goal 2 remains → \"unsolved goals\" not parse error.\n\nHmm, let me look at the error list again: \"150:35: unexpected token '/--'; expected ':='\". Col 35 — line 150 is only 33 chars. So the error position is NOT line 150 of the current file — the compiler's line numbering... could the error be at line 150 counting differently? Line 152 is the /-- doc comment. \"unexpected token '/--'\" — the token IS the doc comment at 152. Its column: the doc comment starts at col 0... \"150:35\" though. Ugh.\n\nLet me try a completely different diagnostic: run lean with more context — get the FULL error output unfiltered for the parse error.","signature":""},{"type":"text","text":"Let me see the full unfiltered error context around the parse failure."},{"type":"tool_use","id":"Bash_291","name":"Bash","input":{"command":"export PATH=\"$HOME/.elan/bin:$PATH\" && cd D:/Python/Quantum/research/lean/NguyenRH1 && lake env lean NguyenRH1/LiCircleBound.lean 2>&1 | grep -B3 -A12 \"unexpected token\" | head -30","description":"Full parse error context","timeout":300000},"extra_content":null}]