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.
Assuming countable choice, the lower-limit line is normal
Statement
Assuming the Axiom of Countable Choice, the lower-limit line is normal.
Facts & Assumptions
Given: The Axiom of Countable Choice.
Under countable choice, the lower-limit line is regular and Lindelöf (The lower-limit line has a clopen basis, is regular, and is Lindelöf under countable choice).
Every regular Lindelöf space is normal (Every regular Lindelöf space is normal).
Proof
Under the stated hypothesis, [L1] supplies a regular Lindelöf lower-limit line.
Applying [L2] gives its normality.
Depends on
Used by
Dependency tree · next 3 levels
Direct dependencies and their dependencies through the next three levels: 56 results over 12 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
- L. A. Steen and J. A. Seebach, Counterexamples in Topology, Sorgenfrey line (standard reference, not scraped)
- Sorgenfrey topology (Encyclopedia of Mathematics) (standard reference, not scraped)