← Session 21 — Tier ii′ planning + launch: close SfBoundProp in Lean (D-064)
thinking (956 chars)
I left sorries in rectInt_deriv_eq_zero — the border membership reasoning is fiddly. Let me think about the cleanest way to do the border parametrization.
The RectangleBorder z w consists of 4 sides:
- bottom: {x + z.im*I | x ∈ [z.re, w.re]}
- top: {x + w.im*I | x ∈ [z.re, w.re]}
- left: {z.re + y*I | y ∈ [z.im, w.im]}
- right: {w.re + y*I | y ∈ [z.im, w.im]}
The vendored Rectangle.lean has RectangleBorder def — let me check its exact form to use it directly.
Actually — this FTC lemma is the fiddliest part of (ii). Alternative approach that avoids the general border membership: parametrize directly. HIntegral (deriv G) z.re w.re z.im: the points x + z.im*I for x ∈ [z.re, w.re] lie on the bottom side — from hG I need differentiability at those points.
Let me check the vendored RectangleBorder definition and mem lemmas (rectangleBorder... from the agent report: `RectangleBorder z w` and mapsTo_rectangle*_NoP lemmas). Let me look at the def.
The FTC lemma needs the exact border structure. Let me check the vendored `RectangleBorder` definition.
tool: Bash
input
{
"command": "grep -n \"def RectangleBorder\\|RectangleBorder \" /d/Python/Quantum/zeta-23-lean/Zeta23/FromPNTPlus/Rectangle.lean | head -8; sed -n \"$(grep -n 'def RectangleBorder' /d/Python/Quantum/zeta-23-lean/Zeta23/FromPNTPlus/Rectangle.lean | head -1 | cut -d: -f1),+15p\" /d/Python/Quantum/zeta-23-lean/Zeta23/FromPNTPlus/Rectangle.lean",
"description": "Read RectangleBorder definition"
}
raw content_json (database row)
[{"type":"thinking","thinking":"I left sorries in rectInt_deriv_eq_zero — the border membership reasoning is fiddly. Let me think about the cleanest way to do the border parametrization.\n\nThe RectangleBorder z w consists of 4 sides:\n- bottom: {x + z.im*I | x ∈ [z.re, w.re]}\n- top: {x + w.im*I | x ∈ [z.re, w.re]}\n- left: {z.re + y*I | y ∈ [z.im, w.im]}\n- right: {w.re + y*I | y ∈ [z.im, w.im]}\n\nThe vendored Rectangle.lean has RectangleBorder def — let me check its exact form to use it directly.\n\nActually — this FTC lemma is the fiddliest part of (ii). Alternative approach that avoids the general border membership: parametrize directly. HIntegral (deriv G) z.re w.re z.im: the points x + z.im*I for x ∈ [z.re, w.re] lie on the bottom side — from hG I need differentiability at those points.\n\nLet me check the vendored RectangleBorder definition and mem lemmas (rectangleBorder... from the agent report: `RectangleBorder z w` and mapsTo_rectangle*_NoP lemmas). Let me look at the def.","signature":""},{"type":"text","text":"The FTC lemma needs the exact border structure. Let me check the vendored `RectangleBorder` definition."},{"type":"tool_use","id":"Bash_221","name":"Bash","input":{"command":"grep -n \"def RectangleBorder\\|RectangleBorder \" /d/Python/Quantum/zeta-23-lean/Zeta23/FromPNTPlus/Rectangle.lean | head -8; sed -n \"$(grep -n 'def RectangleBorder' /d/Python/Quantum/zeta-23-lean/Zeta23/FromPNTPlus/Rectangle.lean | head -1 | cut -d: -f1),+15p\" /d/Python/Quantum/zeta-23-lean/Zeta23/FromPNTPlus/Rectangle.lean","description":"Read RectangleBorder definition"},"extra_content":null}]