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← Session 36 — ii′-6-DL dog-leg + side bounds; Paper A review

#2267 assistant 2026-08-26 17:29:06.294 UTC · 463→948 tok open ⤢
thinking (2711 chars)
Down to ONE error: line 403:8 "No goals to be solved". Line 403 is in the final assembly — the step-5 `congr 1` — congr closed BOTH subgoals (A = A' via... hmm no — A = A' is `∫-T..-10 = ∫10..T` which is hleft — not rfl!). Wait — "No goals to be solved" at 403:8 — let me figure out which line is 403 now. The congr 1 + exact hleft step: if congr 1 closed all goals (maybe congr closed the goal ENTIRELY via defeq?? — the two sides ARE equal up to hleft — not defeq!). Hmm — actually wait: maybe congr 1's auto-rfl closed everything because... no. Let me count: line 403 in the current file. The step-5 block: ``` _ = (∫ t in (10 : ℝ)..T, ...) + ((∫ t in (-10 : ℝ)..(10 : ℝ), ...) + (∫ t in (10 : ℝ)..T, ...)) := by congr 1 exact hleft ``` `congr 1` — then `exact hleft` — if congr 1 closed ALL goals (e.g., it solved A = A' by... no, it can't without hleft)... OR congr 1 produced ONE goal (A = A') and closed the rfl one, and... `exact hleft` says "No goals" — meaning congr 1 closed EVERYTHING. How? congr's auto-rfl uses defeq — A = A' is `∫-T..-10, F = ∫10..T, F` — NOT defeq... UNLESS — congr 1 turned the goal into something trivially closed: maybe congr failed to split and instead closed via... hmm. OR: congr 1 on `HAdd X Y = HAdd X' Y'` — with X = ∫-T..-10 and X' = ∫10..T — it might have used `hleft`?? No — congr doesn't know hleft. Wait — "No goals to be solved" at 403:8 — col 8 — which tactic is at col 8? The `congr 1` line is at col 8 (8 spaces indent). So congr 1 ITSELF reports "No goals to be solved"?! That happens when congr 1 runs with... no goals? Or the error is at `exact hleft` (also col 8, next line). Line numbers: let me count from my edit. The calc starts around line 380. Step 5's `:= by` then `congr 1` then `exact hleft`. If `congr 1` is line 403 and `exact hleft` line 404: the error 403:8 would be congr 1 — but "No goals" for congr means the goal was already closed before it ran?? The `:= by` — the calc step's goal... Hmm — actually maybe the issue: the calc step 5's expected relation got FULLY proved by... no. Alternatively line 403 is `exact hleft` and congr 1 closed everything. Could congr 1 close `A + (B+C) = A' + (B+C)` completely? Its rfl-routine: tries to close subgoals by rfl/defeq — A = A' is NOT defeq... unless congr DIDN'T split (head match failed?) and fell back to trying the whole goal by rfl — fails — then... error would be "congr failed". Hmm. Wait — actually — maybe the calc-step elaboration ORDER: the `:= by` proof is elaborated against the step's expected type `LHS = RHS`. LHS comes from the previous step's RHS (which is my parenthesized form). Hmm. Let me just look at what's on line 403.
One error left at line 403. Checking what's there.
tool: Read
input
{
  "file_path": "D:\\Python\\Quantum\\research\\lean\\NguyenRH1\\NguyenRH1\\LiSideBounds.lean",
  "offset": 378,
  "limit": 35
}
raw content_json (database row)
[{"type":"thinking","thinking":"Down to ONE error: line 403:8 \"No goals to be solved\". Line 403 is in the final assembly — the step-5 `congr 1` — congr closed BOTH subgoals (A = A' via... hmm no — A = A' is `∫-T..-10 = ∫10..T` which is hleft — not rfl!). Wait — \"No goals to be solved\" at 403:8 — let me figure out which line is 403 now. The congr 1 + exact hleft step: if congr 1 closed all goals (maybe congr closed the goal ENTIRELY via defeq?? — the two sides ARE equal up to hleft — not defeq!). Hmm — actually wait: maybe congr 1's auto-rfl closed everything because... no. Let me count: line 403 in the current file. The step-5 block:\n\n```\n    _ = (∫ t in (10 : ℝ)..T, ...) +\n          ((∫ t in (-10 : ℝ)..(10 : ℝ), ...) +\n            (∫ t in (10 : ℝ)..T, ...)) := by\n        congr 1\n        exact hleft\n```\n\n`congr 1` — then `exact hleft` — if congr 1 closed ALL goals (e.g., it solved A = A' by... no, it can't without hleft)... OR congr 1 produced ONE goal (A = A') and closed the rfl one, and... `exact hleft` says \"No goals\" — meaning congr 1 closed EVERYTHING. How? congr's auto-rfl uses defeq — A = A' is `∫-T..-10, F = ∫10..T, F` — NOT defeq... \n\nUNLESS — congr 1 turned the goal into something trivially closed: maybe congr failed to split and instead closed via... hmm. OR: congr 1 on `HAdd X Y = HAdd X' Y'` — with X = ∫-T..-10 and X' = ∫10..T — it might have used `hleft`?? No — congr doesn't know hleft.\n\nWait — \"No goals to be solved\" at 403:8 — col 8 — which tactic is at col 8? The `congr 1` line is at col 8 (8 spaces indent). So congr 1 ITSELF reports \"No goals to be solved\"?! That happens when congr 1 runs with... no goals? Or the error is at `exact hleft` (also col 8, next line). Line numbers: let me count from my edit. The calc starts around line 380. Step 5's `:= by` then `congr 1` then `exact hleft`. If `congr 1` is line 403 and `exact hleft` line 404: the error 403:8 would be congr 1 — but \"No goals\" for congr means the goal was already closed before it ran?? The `:= by` — the calc step's goal... \n\nHmm — actually maybe the issue: the calc step 5's expected relation got FULLY proved by... no.\n\nAlternatively line 403 is `exact hleft` and congr 1 closed everything. Could congr 1 close `A + (B+C) = A' + (B+C)` completely? Its rfl-routine: tries to close subgoals by rfl/defeq — A = A' is NOT defeq... unless congr DIDN'T split (head match failed?) and fell back to trying the whole goal by rfl — fails — then... error would be \"congr failed\". Hmm.\n\nWait — actually — maybe the calc-step elaboration ORDER: the `:= by` proof is elaborated against the step's expected type `LHS = RHS`. LHS comes from the previous step's RHS (which is my parenthesized form). Hmm.\n\nLet me just look at what's on line 403.","signature":""},{"type":"text","text":"One error left at line 403. Checking what's there."},{"type":"tool_use","id":"Read_56","name":"Read","input":{"file_path":"D:\\Python\\Quantum\\research\\lean\\NguyenRH1\\NguyenRH1\\LiSideBounds.lean","offset":378,"limit":35},"extra_content":null}]