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.
Dimension, openness, norm, Jacobian, and the native Euclidean linear-map agreement seam
The derivative definition is stated on open Euclidean domains so every sufficiently small increment is admissible. Its remainder uses the Euclidean norm; in finite-dimensional Euclidean spaces an equivalent norm would give the same differentiability notion, but that change is not part of this definition.
The linear-map definition on this page is deliberately the concrete Euclidean special case identified in Conventions of this page, the standing hypothesis, and what is taken up elsewhere in the reading order. A future general linear-map development must prove agreement with A linear map in Euclidean coordinates, not silently replace the meaning of .
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
34 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.
Sources
- J. Lebl, Basic Analysis I, §8.3 (standard reference, not scraped)