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

#1540 assistant 2026-08-23 17:43:08.380 UTC · 1533→1274 tok open ⤢
thinking (3942 chars)
"150:35: unexpected token '/--'; expected ':='" — column 35 of line 150... ` linarith [ih, hwin, hle1, hle2]` has 35 characters total! So position 150:35 is END of that line. The parser says: after `linarith [ih, hwin, hle1, hle2]`... it expected `:=`?? That means `linarith` was parsed as the START of a declaration (a def/lemma name!) — "unknown identifier linarith" confirms: at that point we're at TOP LEVEL (command parser), and `linarith [ih, hwin, hle1, hle2]` is parsed as a command `linarith` with `[...]`... and the next token `--` expected `:=`. So the tactic block ENDED before line 150 — the succ-case by-block was closed after line 149's `linarith` (hle2's last tactic)... but line 149's linarith is INSIDE hle2's by-block (indent 6), and hle2's block... wait — if hle2's by-block closed at line 149 and ALSO the succ-case sequence is done — but line 150 has indent 4, matching the case body. If the case body had a complete tactic sequence ending at 149, then line 150 would be... no — the case body is a SINGLE tactic sequence; it can't "complete" mid-way — the parser reads tactics until something that doesn't parse as a tactic. Line 149 ` linarith` (hle2's final tactic, indent 6 — INSIDE hle2's by-block which has tactics at indent 6). Then line 150 ` linarith [...]` indent 4 — LESS than hle2's block indent 6 ⟹ hle2's block ends; indent 4 = the succ case's body level ⟹ should parse as the next tactic of the case ✓... Hmm UNLESS hle2's by-block is malformed: `apply Real.log_le_log (by positivity)` then `have h1 : ... := (...)` then `linarith` — if `apply Real.log_le_log (by positivity)` SOLVED the whole goal?? No — it can't (the x ≤ y goal remains). Wait — actually — could the issue be that line 149's `linarith` CLOSED hle2's remaining goal, and then ` linarith [ih, hwin, hle1, hle2]` at line 150 — hmm but that's exactly what should happen. Let me reconsider: the error "150:35: unexpected token '/--'; expected ':='" — the '/--' token is the DOC COMMENT at line 152! So the parser at line 152's doc comment expected ':=' — meaning the parser read line 150-151 as `linarith [ih, hwin, hle1, hle2]` — a COMMAND — and doc comments attach to commands; the command `linarith [attrs]`... an unknown command followed by a doc comment — the parser says "expected :=" treating `linarith [ih, hwin, hle1, hle2] /-- doc -/` as a malformed declaration!! So the question remains why line 150 is parsed as top-level. The answer must be: the succ-case's tactic SEQUENCE terminated after line 149. Because hle2's by-block ended AND the case-body had already ended?? How — OH WAIT. I see it — line 143-149: ``` have hle2 : ... := by apply mul_le_mul_of_nonneg_left _ A0count_pos.le apply Real.log_le_log (by positivity) have h1 : ... := (abs_add_le _ _).trans (by rw [...]) linarith ``` Hmm that's fine... let me reconsider — MAYBE the problem is in hle1's calc block! The calc: ``` calc A0count * (N : ℝ) * Real.log (|a| + (N : ℝ) + 3) ≤ A0count * ((N : ℝ) + 1) * Real.log (|a| + ((N : ℝ) + 1) + 3) := by have hA0 := A0count_pos.le ... ``` The calc's step `≤ ... := by` — with the by-block at indent 12 — the calc's structure: first line at indent 6, continuation at 10. When the by-block inside ends, the next line at indent 4 (`have hle2`) — the calc is complete ✓... Hmm hold on — maybe the actual culprit: `have hA0 := A0count_pos.le` — `A0count_pos.le` — is that valid? A0count_pos : 0 < A0count — `.le` : LT.lt.le projection ✓ fine. Let me test the parse theory by simply looking at what's special — actually, let me try a targeted experiment: replace the final `linarith [ih, hwin, hle1, hle2]` with an explicit calc-free chain to see if the parse error moves. Actually quicker: check whether the issue is the TAB/space mix or an invisible character in the file around line 150! Let me hexdump-check the line endings around 145-152.
The parser treats line 150 as top-level — the tactic block is being terminated early. Let me check for invisible characters/indentation issues in that region.
tool: Bash
input
{
  "command": "cd D:/Python/Quantum/research/lean/NguyenRH1 && sed -n '142,152p' NguyenRH1/LiCircleBound.lean | cat -A | head -15",
  "description": "Inspect raw bytes of the failing region"
}
raw content_json (database row)
[{"type":"thinking","thinking":"\"150:35: unexpected token '/--'; expected ':='\" — column 35 of line 150... `    linarith [ih, hwin, hle1, hle2]` has 35 characters total! So position 150:35 is END of that line. The parser says: after `linarith [ih, hwin, hle1, hle2]`... it expected `:=`?? That means `linarith` was parsed as the START of a declaration (a def/lemma name!) — \"unknown identifier linarith\" confirms: at that point we're at TOP LEVEL (command parser), and `linarith [ih, hwin, hle1, hle2]` is parsed as a command `linarith` with `[...]`... and the next token `--` expected `:=`. So the tactic block ENDED before line 150 — the succ-case by-block was closed after line 149's `linarith` (hle2's last tactic)... but line 149's linarith is INSIDE hle2's by-block (indent 6), and hle2's block... wait — if hle2's by-block closed at line 149 and ALSO the succ-case sequence is done — but line 150 has indent 4, matching the case body. If the case body had a complete tactic sequence ending at 149, then line 150 would be... no — the case body is a SINGLE tactic sequence; it can't \"complete\" mid-way — the parser reads tactics until something that doesn't parse as a tactic. Line 149 `      linarith` (hle2's final tactic, indent 6 — INSIDE hle2's by-block which has tactics at indent 6). Then line 150 `    linarith [...]` indent 4 — LESS than hle2's block indent 6 ⟹ hle2's block ends; indent 4 = the succ case's body level ⟹ should parse as the next tactic of the case ✓...\n\nHmm UNLESS hle2's by-block is malformed: `apply Real.log_le_log (by positivity)` then `have h1 : ... := (...)` then `linarith` — if `apply Real.log_le_log (by positivity)` SOLVED the whole goal?? No — it can't (the x ≤ y goal remains).\n\nWait — actually — could the issue be that line 149's `linarith` CLOSED hle2's remaining goal, and then `    linarith [ih, hwin, hle1, hle2]` at line 150 — hmm but that's exactly what should happen. Let me reconsider: the error \"150:35: unexpected token '/--'; expected ':='\" — the '/--' token is the DOC COMMENT at line 152! So the parser at line 152's doc comment expected ':=' — meaning the parser read line 150-151 as `linarith [ih, hwin, hle1, hle2]` — a COMMAND — and doc comments attach to commands; the command `linarith [attrs]`... an unknown command followed by a doc comment — the parser says \"expected :=\" treating `linarith [ih, hwin, hle1, hle2] /-- doc -/` as a malformed declaration!! So the question remains why line 150 is parsed as top-level.\n\nThe answer must be: the succ-case's tactic SEQUENCE terminated after line 149. Because hle2's by-block ended AND the case-body had already ended?? How — OH WAIT. I see it — line 143-149:\n```\n    have hle2 : ... := by\n      apply mul_le_mul_of_nonneg_left _ A0count_pos.le\n      apply Real.log_le_log (by positivity)\n      have h1 : ... := (abs_add_le _ _).trans (by rw [...])\n      linarith\n```\nHmm that's fine... let me reconsider — MAYBE the problem is in hle1's calc block! The calc:\n```\n      calc A0count * (N : ℝ) * Real.log (|a| + (N : ℝ) + 3)\n          ≤ A0count * ((N : ℝ) + 1) * Real.log (|a| + ((N : ℝ) + 1) + 3) := by\n            have hA0 := A0count_pos.le\n            ...\n```\nThe calc's step `≤ ... := by` — with the by-block at indent 12 — the calc's structure: first line at indent 6, continuation at 10. When the by-block inside ends, the next line at indent 4 (`have hle2`) — the calc is complete ✓...\n\nHmm hold on — maybe the actual culprit: `have hA0 := A0count_pos.le` — `A0count_pos.le` — is that valid? A0count_pos : 0 < A0count — `.le` : LT.lt.le projection ✓ fine.\n\nLet me test the parse theory by simply looking at what's special — actually, let me try a targeted experiment: replace the final `linarith [ih, hwin, hle1, hle2]` with an explicit calc-free chain to see if the parse error moves. Actually quicker: check whether the issue is the TAB/space mix or an invisible character in the file around line 150! Let me hexdump-check the line endings around 145-152.","signature":""},{"type":"text","text":"The parser treats line 150 as top-level — the tactic block is being terminated early. Let me check for invisible characters/indentation issues in that region."},{"type":"tool_use","id":"Bash_292","name":"Bash","input":{"command":"cd D:/Python/Quantum/research/lean/NguyenRH1 && sed -n '142,152p' NguyenRH1/LiCircleBound.lean | cat -A | head -15","description":"Inspect raw bytes of the failing region"},"extra_content":null}]