Mathlib v4.30 source proposition Nat.gcd_greatest

Identifier: F:ml430-nat-gcd-greatest-0a04214a
Proof route: kernel-lean
External status: proved
Axiom footprint: Empty

Recorded description

The proposition declared as `Nat.gcd_greatest` in the pinned Mathlib v4.30 source.

Formal statement

∀ {a b d : ℕ}, d ∣ a → d ∣ b → (∀ (e : ℕ), e ∣ a → e ∣ b → e ∣ d) → d = a.gcd b

Dependencies

The graph shows direct ledger edges. Follow a node to open its artifact page.

0 direct dependencies 0 direct dependents

Evidence

autogenesis-operation-b6e41f105f3c9f9b

Kind: kernel-term
Status: checked

Supports: The proposition declared as `Nat.gcd_greatest` in the pinned Mathlib v4.30 source.

Checker command

python3 scripts/check-autogenesis-fact-operation.py --fact artifacts/facts/F-ml430-nat-gcd-greatest-0a04214a.json

Evidence notes

Derived from a clean-commit typed execution receipt. The registered fact-operation checker replays the immutable capsule and committed result manifest and requires their exact twice-reconstructed theorem identity, empty axiom footprint, and named direct theorem dependencies; no caller-authored route, footprint, checker, or shell command is accepted.

Provenance

{
  "date": "2026-08-18",
  "established_by": "axeyum-autogenesis execution b5732ffdd87f7c04b8464073c525052d7c3d368aca4acb5238781f5d68461075",
  "prior_art": [
    {
      "attribution": "the proposition was read from the pinned statement-only inventory; the proof term and tactic trace were not consulted",
      "what": "the theorem declaration `Nat.gcd_greatest`",
      "where": "mathlib4 commit c5ea00351c28e24afc9f0f84379aa41082b1188f (v4.30.0)",
      "who": "the Mathlib contributors",
      "year": 2026
    }
  ],
  "source": "statement-only extraction of `Nat.gcd_greatest` from Mathlib v4.30.0; no proof value was exposed"
}