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.
Every finite extension of a perfect field is simple
Statement
Every finite extension of a perfect field is simple.
Facts & Assumptions
Given: A finite extension with perfect.
Every finite field extension is algebraic (Every finite field extension is algebraic).
Every algebraic extension of a perfect field is separable (Every algebraic extension of a perfect field is separable).
Every finite separable extension is simple (A finite extension generated by elements all but possibly one of which are separable is simple).
Proof
By [L1] the extension is algebraic, and [L2] therefore makes it separable.
It is finite and separable, so [L3] makes it simple.
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
13 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
- J. S. Milne, Fields and Galois Theory, Chapter 5 (standard reference, not scraped)