TheoremStatement: Literature-sourcedProof: AI-adaptedprecheck passjudge pass (deepseek-v4-pro + claude-sonnet-5)audited 2026-08-17

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.

Separable degree is multiplicative in finite towers: $[L : F]_{s} = [L : K]_{s} [K : F]_{s}$

For every finite tower $F \subseteq K \subseteq L$ ,

$[L : F]_{s} = [L : K]_{s} [K : F]_{s} .$

Given: A finite tower $F \subseteq K \subseteq L$ and an algebraic closure $Ω / F$ .

[L1]

[L2]

Restriction from $F$ -embeddings of $L$ to $F$ -embeddings of $K$ is surjective, and every fibre has cardinality $[L : K]_{s}$ (Restriction partitions embeddings in a finite tower into extension fibres).

technique · direct

1.1L2

By [L2], the finite set ${Hom}_{F} (L, Ω)$ is the disjoint union of the restriction fibres indexed by ${Hom}_{F} (K, Ω)$ .

2.1step 1.1L1L2algebra∎

There are $[K : F]_{s}$ fibres by [L1], and each has $[L : K]_{s}$ elements by [L2]. Counting the disjoint union gives the displayed product.

Depends on