DefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (gpt-5.6-terra)audited 2026-08-30

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.

Families of holomorphic functions omitting two common finite values

Definition

Let $Ω$ be a plane domain and $F \subseteq H (Ω)$ . The family $F$ is a two-value-omitting holomorphic family when there are distinct $a, b \in C$ such that

$f (Ω) \cap {a, b} = \emptyset (f \in F) .$

By postcomposing with an affine map, one may normalize the omitted pair to ${0, 1}$ when convenient.

Used by

Families omitting two values are chordally normal Theorem

Dependency tree · 0 levels

Nothing. This result depends on no other item in the library.

Sources

Aleksander Simonic, The Ahlfors lemma and Picard's theorems, Theorem 13 (standard reference, not scraped)