Alphabeta Math
ExampleConstruction: Literature-sourcedVerification: AI-adaptedPipeline-generatedjudge pass (gpt-5.6-terra)audited 2026-09-14
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.

Finite support forces a finite-or-cofinite atom subset

Statement

A subset of the basic Fraenkel atoms supported by E is contained in E or contains every atom outside E.

Facts & Assumptions

Given: The hypotheses, objects, and conventions in the Statement.

[F1]

The basic Fraenkel model gives the full permutation action and finite-support rule.

Proof

1.1

Let B⊆A be supported by finite E. If some a∉E lies in B, then for every b∉E the transposition (a b) fixes E and hence B, so b∈B. Thus A∖E⊆B and B is cofinite.

F1
2.1

If no such a exists, then B⊆E and B is finite. This includes the vacuous case A∖E=∅, although it cannot occur when A is infinite and E finite.

F1step 1.1∎

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