Alphabeta Math
False statementConstruction: Literature-sourcedVerification: AI-generatedprecheck passjudge pass (gpt-5.6-terra)audited 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.

FALSE: a regular expression is the same object as its denoted language

Statement

False claim: every regular expression is literally the same object as the language it denotes.

Facts & Assumptions

Given: The regular expression a+b over the alphabet {a,b}.

[A1]

The statement refuted is: every regular expression is literally the same object as the language it denotes.

[L1]

By Regular expression syntax over an alphabet, a+b is a formal expression built from two letter expressions by one application of the union constructor.

[L2]

By The language denoted by a regular expression, the language denoted by a+b is {a,b}.

Refutation

technique · direct
1.1

The object a+b is, by [L1], a syntactic expression tree with an outer union node and two letter leaves.

L1given
2.1

The object L(a+b) is, by [L2], the two-element set {a,b} of words.

L2step 1.1
3.1

A formal expression tree and a two-element set of words are not literally the same kind of object, so [A1] is false.

A1step 1.1step 2.1∎

Depends on

Used by

Dependency tree · two levels

6 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