Alphabeta MathHow 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.
Britton reduction of a word with two pins
Example
In associated-subgroup notation, the word
contains two pins and Britton-reduces to the base-group element .
Facts & Assumptions
Given: An HNN extension in associated-subgroup notation.
The displayed subwords and are pins. (HNN words, pins, and Britton-reduced words)
Replacing either kind of pin by the corresponding subgroup element preserves the represented element. (Elementary HNN reductions preserve the represented element)
Britton's lemma detects nontriviality only after all pins have been removed. (Britton's lemma)
Verification
By [L1], the first three letters of form a pin, so [L2] replaces them by and gives the shorter word .
The remaining stable-letter subword is the second kind of pin, so another application of [L2] gives . This is the Britton-reduced representative to which [L3] applies.
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
- Roger C. Lyndon and Paul E. Schupp, Combinatorial Group Theory (standard reference, not scraped)