ExampleConstruction: AI-generatedVerification: AI-generatedjudge pass (z-ai/glm-5.2)audited 2026-07-31

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.

Under choice, a concrete ccc nonseparable Cantor cube indexed above $2^{ℵ_{0}}$

Example

Let $I = P (P (N))$ . Cantor's theorem gives $∣ I ∣ > 2^{ℵ_{0}}$ . Under choice, Under choice, every Cantor cube $2^{I}$ satisfies ccc makes $2^{I}$ ccc and Under choice, if $∣ I ∣ > 2^{ℵ_{0}}$ , then the Cantor cube $2^{I}$ is not separable makes it nonseparable.

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

20 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

UCR General Topology Notes (standard reference, not scraped)
Cantor cube (Wikipedia) (standard reference, not scraped)

Under choice, a concrete ccc nonseparable Cantor cube indexed above 2ℵ02ℵ0​