RemarkRemark: AI-adaptedProof: Not applicableSession-authored (Fable 5 assisted)audited 2026-08-02

How 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 $n \ge 1$ hypothesis, and what is taken up elsewhere in the reading order. A future general linear-map development must prove agreement with A linear map $L:\mathbb{R}^m\to\mathbb{R}^n$ in Euclidean coordinates, not silently replace the meaning of $Df(a)$ .

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: 170 results over 25 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 I, §8.3 (standard reference, not scraped)