Mathlib theorem · Existing formal mathematics

Lean verification record

Checked Artifact: Dirichlet's Theorem on Primes in Arithmetic Progressions (mathlib)

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

Verification result

The recorded Lean checks passed

  • Build replaypassed with retained transcript
  • Unfinished stepsNone found
  • Source identityPinned commit and file recorded
  • Dependency profileAxiom closure recorded

Reproducibility details

What the checker recorded

Declaration checked
Nat.infinite_setOf_prime_and_eq_mod
Module
Mathlib.NumberTheory.LSeries.PrimesInAP
Source file checked
Mathlib/NumberTheory/LSeries/PrimesInAP.lean
Package commit
5e932f97dd25535344f80f9dd8da3aab83df0fe6
Build transcript
passed · retained with this record
Unfinished proof steps
None found by the recorded no-sorry scan
Axiom closure
Classical.choice, Quot.sound, propext
Collection provenance
Clean source state recorded

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

Mathlib is the source of the theorem; the local Lean replay and page review are separate.

Evidence boundary

Exact formal statement only

This target indexes Mathlib's infinitude theorem for primes in one invertible residue class modulo a nonzero natural modulus. It asserts infinitely many such primes; it does not give their density, an asymptotic counting formula, a least-prime bound, or a new proof.

This checker record does not establish novelty, transfer a historical acceptance decision, or authorize publication.