Alphabeta Math
TheoremStatement: Literature-sourcedProof: AI-adaptedSession-authored (Fable 5 assisted)precheck passjudge pass (deepseek-v4-pro + gpt-5.6-terra)audited 2026-08-16
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.

Tower law for finite extensions: [L:F]=[L:K][K:F]

Statement

Let F⊆K⊆L be fields. If K/F and L/K are finite, then L/F is finite and

[L:F]=[L:K][K:F].

Facts & Assumptions

Given: Finite extensions K/F and L/K.

[L1]

Products of an F-basis of K and a K-basis of L form an F-basis of L (Products of bases form a basis in a tower of finite extensions).

[L2]

Extension degree is the size of a finite basis (The degree [K:F]=dim⁡FK of a finite field extension).

Proof

technique · direct
1.1

Choose bases of sizes m=[K:F] and n=[L:K].

givenL2choose
2.1

By [L1], their mn pairwise products form an F-basis of L.

step 1.1L1
3.1

Hence L/F is finite and [L2] gives [L:F]=mn=[L:K][K:F].

step 2.1L2algebra∎

Depends on

Used by

Dependency tree · next 3 levels

Direct dependencies and their dependencies through the next three levels: 28 results over 11 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