Technical Lean evidence record
Checked Artifact: Downward Löwenheim–Skolem 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
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
FirstOrder.Language.exists_elementarySubstructure_card_eq- Module
Mathlib.ModelTheory.Skolem- Source file checked
Mathlib/ModelTheory/Skolem.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 Downward Löwenheim–Skolem theorem for a nonempty first-order L-structure M, a prescribed seed set s, and an infinite cardinal κ. After the explicit universe lifts, the seed and language cardinalities must be at most κ and κ must be at most the ambient cardinality. The endpoint gives an elementary L-substructure containing s with lifted cardinality exactly κ. It is not an unrestricted countable-submodel claim or the upward theorem.
This checker record is evidence for the exact formal statement only. It does not establish novelty, transfer a historical acceptance decision, or authorize publication.