Mathlib v4.30 source proposition Nat.modulus_modEq_zero

Identifier: F:ml430-nat-modulus-modeq-zero-fd9af096
Proof route: kernel-lean
External status: proved
Axiom footprint: Empty

Recorded description

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

Formal statement

∀ {n : ℕ}, n ≡ 0 [MOD n]

Dependencies

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0 direct dependencies 0 direct dependents

Evidence

autogenesis-operation-bf6495de17753819

Kind: kernel-term
Status: checked

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

Checker command

python3 scripts/check-autogenesis-fact-operation.py --fact artifacts/facts/F-ml430-nat-modulus-modeq-zero-fd9af096.json

Evidence notes

Derived from a clean-commit typed execution receipt. The registered fact-operation checker replays the resolves immutable target and candidate streams through the operation's reviewed checker and requires the exact kernel-checked proof, one named retained theorem dependency, and no target dependency; no caller-authored route, footprint, checker, or shell command is accepted.

Provenance

{
  "date": "2026-08-18",
  "established_by": "axeyum-autogenesis execution cd5664fd878eb9467c34d7f360400b03483897e0493e4dc5f2e7d31c67754b42",
  "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.modulus_modEq_zero`",
      "where": "mathlib4 commit c5ea00351c28e24afc9f0f84379aa41082b1188f (v4.30.0)",
      "who": "the Mathlib contributors",
      "year": 2026
    }
  ],
  "source": "statement-only extraction of `Nat.modulus_modEq_zero` from Mathlib v4.30.0; no proof value was exposed"
}