Technical Lean evidence record

Checked Artifact: Primitive Element Theorem (mathlib)

Proof Atlas collected build, no-sorry, axiom, and clean-source evidence directly from the pinned upstream declaration.

ProofAtlas record

What has been checked

Upstream indexedPinned source bytes verified locally

Locally reproducedExact upstream declaration replayed

Reviewed pageCurrent public presentation reviewed

Accepted Atlas resultNot recorded for the preferred artifact

These states distinguish upstream identity, local reproduction, review, and Atlas acceptance. This page is part of the public, read-only Mathlib landmark collection.

Mechanical evidence

Declaration checked: Field.exists_primitive_element
Module: Mathlib.FieldTheory.PrimitiveElement
Source file checked: Mathlib/FieldTheory/PrimitiveElement.lean
Package commit: 5e932f97dd25535344f80f9dd8da3aab83df0fe6
Build: passed · transcript retained
Unfinished proof steps: None found by the recorded no-sorry scan
Axiom closure: Classical.choice, Quot.sound, propext
Clean collection provenance: Recorded

Evidence boundary

This target indexes Mathlib's existence theorem for a primitive element of a finite-dimensional separable field extension E/F: some α : E satisfies F⟮α⟯ = ⊤. Finite means finite-dimensional, not finite cardinality. The result does not assert uniqueness or canonicity of α and does not cover general inseparable extensions.

This checker record is evidence for the exact formal statement only. It does not establish novelty, transfer a historical acceptance decision, or authorize publication.