Alphabeta MathHow statement and proof provenance work
The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.
- Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
- AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
- AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.
These labels describe origin, not correctness: citations and verification chips remain separate evidence.
Limitation: arbitrary Jordan domains are not covered by the elementary Green theorem
The theorem Green's theorem for finite unions of elementary regions applies only when an elementary decomposition and the stated finite gluing data are supplied. It neither constructs the interior of an arbitrary Jordan curve nor proves that such an interior admits this decomposition. The general Jordan-domain theorem requires additional curve-separation and decomposition results, so it is not asserted here.
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · next 3 levels
Direct dependencies and their dependencies through the next three levels: 28 results over 10 levels. An arrow runs from a result to what uses it, and this result sits at the bottom with a heavier outline. Click the chart to enlarge it.
Sources
- J. Lebl, Basic Analysis II, section 10.6 (standard reference, not scraped)