Alphabeta Math
False statementConstruction: AI-adaptedVerification: AI-generatedPipeline-generatedprecheck passaudited 2026-08-28
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.

FALSE: a normal family contains every locally uniform sequential limit of its own sequences

Statement

A normal family contains every locally uniform limit of its own sequences.

Facts & Assumptions

Given: The family F={zn:n≥1} on the unit disc.

[L1]

The family {zn:n≥1} is normal on D, but its full sequence converges locally uniformly to 0 (The family z^n is normal on the unit disc and not normal on the complex plane).

Refutation

technique · direct
1.1

Fact [L1] gives a normal family whose defining sequence has local uniform limit 0.

L1given
2.1

The zero function is not one of the nonzero powers zn, so the limit does not lie in the family. Hence the statement is false.

given∎

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

5 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