DefinitionDefinition: AI-adaptedProof: Not applicableaudited 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.

A supporting line of slope $m$ for a real function at an interior point

Definition

Let $f : I \to R$ , where $I$ is an interval (Intervals of $R$ : the nine order-convex forms, nondegeneracy, and length), and let $c$ be an interior point of $I$ . A line of slope $m$ supports $f$ at $c$ when

$f (x) \geq f (c) + m (x - c)$

for every $x \in I$ . The supporting line is the affine function $x \mapsto f (c) + m (x - c)$ .

Depends on

Intervals of $R$ : the nine order-convex forms, nondegeneracy, and length

Dependency tree · 2 levels

Sources

R. Gardner, Convex Functions, Notes 6.6