Files
curriculum-project-hub/render/examples/smoke-eng/lemmas/柯西不等式/proof.typ
T
sjfhsjfh 7e15cf34f6 feat(render): export templates + render-lesson entry; template owns include loop (WU-C', ADR-0011)
Replace the display(parts) entry (which a generated driver called) with the
template model: real editable templates (render/templates/{student,teacher}.typ,
the framework defaults copied into an engineering file's exports/) read the
manifest via toml(sys.inputs.manifest) and assemble parts themselves.

Key finding (drives the engine): a dynamic `include` inside a package resolves
against the PACKAGE root, never --root — so the include loop must live in the
TEMPLATE (which sits under --root): `include "/" + part.path + "/" + field +
".typ"` (root-relative absolute, runtime-computed — legal per ADR-0011's verified
fact). cph-render exposes render-lesson(info, target, parts, heading-numbering)
(content-in, never includes) + part-fields (kind→fields) + default-heading-numbering.
Numbering (numbly per-level) is set in the template, editable per engineering file.

Surfaced OPEN point closed by the engine (WU-D'): typst has no file-exists
primitive, so optional content (lemma proof) presence comes from a per-part
`fields` array the engine computes from disk. Manifest injected as root-relative
absolute (--input manifest=/...). numbly stays vendored/offline. display removed.

local-packages symlink (test-only @local resolution) gitignored — regenerable,
self-referential; the embedded engine mounts cph-render directly.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
2026-06-22 09:57:51 +08:00

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由数量积定义 $arrow(a) dot arrow(b) = |arrow(a)| |arrow(b)| cos theta$
$|cos theta| <= 1$,故 $|arrow(a) dot arrow(b)| = |arrow(a)| |arrow(b)| |cos theta| <= |arrow(a)| |arrow(b)|$
$qed$