← Session 35 — ii′-6-R: Lagarias 6.1 right-tail re-proof (E-032/D-073)
thinking (981 chars)
Interesting — the goal is now:
```
star(kFun n s) * -(star(deriv ζ s)/star(ζ s)) = star(kFun n s) * -(starRingEnd ℂ (deriv ζ s / ζ s))
```
and simp only [map_mul, map_neg] rewrote the outer pieces but map_div "unused" — meaning simp's matching for map_div ALSO failed on `starRingEnd ℂ (deriv riemannZeta s / riemannZeta s)`. That's really strange — it's literally `f (a / b)`.
Hypothesis: in this Mathlib version, `map_div` might be about `NNRat`/`NNReal` division or it's `map_div` for `Div` in ordered fields requiring [FunLike F α β] [MonoidWithZeroHomClass]... The division on ℂ is `Div.div` from `DivInvMonoid`. map_div for group-with-zero homs: `map_div (f : G →* G')`? starRingEnd ℂ : ℂ →+* ℂ is a RingHom — is there a coercion path making map_div not see it as a monoid hom? The application `(starRingEnd ℂ) x` is `RingHom.coe`... map_div's LHS is `⇑f (a/b)` where ⇑ is the FunLike coe — should match syntactically.
Let me just check what map_div says in this Mathlib:
`map_div` is matching nothing in this Mathlib — checking its actual signature.
tool: Bash
input
{
"command": "cd D:/Python/Quantum/zeta-23-lean && grep -rn \"theorem map_div\\b\\|lemma map_div\\b\" .lake/packages/mathlib/Mathlib/Algebra/ 2>/dev/null | head -5",
"description": "Find map_div signatures in Mathlib"
}
raw content_json (database row)
[{"type":"thinking","thinking":"Interesting — the goal is now:\n\n```\nstar(kFun n s) * -(star(deriv ζ s)/star(ζ s)) = star(kFun n s) * -(starRingEnd ℂ (deriv ζ s / ζ s))\n```\n\nand simp only [map_mul, map_neg] rewrote the outer pieces but map_div \"unused\" — meaning simp's matching for map_div ALSO failed on `starRingEnd ℂ (deriv riemannZeta s / riemannZeta s)`. That's really strange — it's literally `f (a / b)`.\n\nHypothesis: in this Mathlib version, `map_div` might be about `NNRat`/`NNReal` division or it's `map_div` for `Div` in ordered fields requiring [FunLike F α β] [MonoidWithZeroHomClass]... The division on ℂ is `Div.div` from `DivInvMonoid`. map_div for group-with-zero homs: `map_div (f : G →* G')`? starRingEnd ℂ : ℂ →+* ℂ is a RingHom — is there a coercion path making map_div not see it as a monoid hom? The application `(starRingEnd ℂ) x` is `RingHom.coe`... map_div's LHS is `⇑f (a/b)` where ⇑ is the FunLike coe — should match syntactically.\n\nLet me just check what map_div says in this Mathlib:","signature":""},{"type":"text","text":"`map_div` is matching nothing in this Mathlib — checking its actual signature."},{"type":"tool_use","id":"Bash_183","name":"Bash","input":{"command":"cd D:/Python/Quantum/zeta-23-lean && grep -rn \"theorem map_div\\b\\|lemma map_div\\b\" .lake/packages/mathlib/Mathlib/Algebra/ 2>/dev/null | head -5","description":"Find map_div signatures in Mathlib"},"extra_content":null}]