Alphabeta Math
CounterexampleConstruction: AI-generatedVerification: AI-generatedprecheck passaudited 2026-09-12
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.

The expression a+b is not literally the set {a,b}

Statement refuted

The false statement claims that a regular expression is literally the same object as the language it denotes.

Facts & Assumptions

Given: The regular expression a+b.

[L1]

By FALSE: a regular expression is the same object as its denoted language, the refuted claim is that a regular expression is literally the same object as its denoted language.

Counterexample

technique · direct
1.1

The object a+b is a formal expression, while its denotation is the language {a,b}.

given
2.1

A formal expression and a two-element set of words are not literally the same object, so the example contradicts the claim in [L1].

L1step 1.1∎

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

3 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