Mathlib v4.30 source proposition Nat.ModEq.refl

Identifier: F:ml430-nat-modeq-refl-d870c8f5
Proof route: kernel-lean
External status: proved
Axiom footprint: Empty

Recorded description

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

Formal statement

∀ {n : ℕ} (a : ℕ), a ≡ a [MOD n]

Dependencies

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

0 direct dependencies 0 direct dependents

Evidence

autogenesis-operation-nat-modeq-1c0507f1ded168f7

Kind: kernel-term
Status: checked

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

Checker command

python3 scripts/check-autogenesis-nat-modeq-family.py

Evidence notes

Derived from an independently replayed modeq-family receipt. The registered fact-operation checker (scripts/check-autogenesis-nat-modeq-family.py) replays the proof-isolated statement artifact through a fresh importer and requires the exact kernel-checked proof and dependency-free result; no caller-authored route, footprint, checker, or shell command is accepted. This is a BLIND GENERALIZATION of the train-set producer (modeq_family_support, tuned only on the four int-modeq-* streams and committed unmodified): it unfolds `Nat.ModEq.refl`'s definitional `ModEq n a b := a % n = b % n` and closes with Eq.refl, reconstructed directly from Eq.rec -- never a borrowed theorem, never a reference to the target or a sibling ModEq fact. Only THIS fact of the three the operation names is settled here; `F:ml430-nat-modeq-symm-0a3d4d18` and `F:ml430-nat-modeq-trans-ef9d1c46` remain open and dispatchable, deliberately left for a following lane so the transition stays reviewable one fact at a time.

Provenance

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