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.
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- 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.
The complex numbers form an algebraic closure of
Statement
The field extension is an algebraic closure of .
Facts & Assumptions
Given: The field extension .
The field is algebraically closed (The complex numbers are algebraically closed).
The complex field is a simple algebraic extension of of degree ( has power basis and degree ).
An algebraic closure of a field is an algebraic extension whose top field is algebraically closed (An algebraic closure of a field).
Proof
Fact [L1] gives the algebraically closed part of the definition in [L3].
Fact [L2] gives the algebraic-extension part of the definition in [L3].
Therefore [L3] makes an algebraic closure of .
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
25 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, v5.10, Corollary 5.7(a) (standard reference, not scraped)