Mathlib v4.30 source proposition Nat.ModEq.comm

Identifier: F:ml430-nat-modeq-comm-24b71e7a
Proof route: kernel-lean
External status: proved
Axiom footprint: Empty

Recorded description

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

Formal statement

∀ {n a b : ℕ}, a ≡ b [MOD n] ↔ b ≡ a [MOD n]

Dependencies

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1 direct dependencies 0 direct dependents

Evidence

autogenesis-operation-80dc2c09437382bf

Kind: kernel-term
Status: checked

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

Checker command

python3 scripts/check-autogenesis-fact-operation.py --fact artifacts/facts/F-ml430-nat-modeq-comm-24b71e7a.json

Evidence notes

Derived from a clean-commit typed execution receipt. The registered fact-operation checker replays the resolved multi-target statement adapter and candidate manifests through the operation's own reviewed checker module and requires the exact kernel-checked proof, dependency-free result, and matching target definition; no caller-authored route, footprint, checker, or shell command is accepted.

Provenance

{
  "date": "2026-08-18",
  "established_by": "axeyum-autogenesis execution 90abe6eb1335ee93eef2bf53d289f4c5e89e43585b2280aa854d8e00e891e443",
  "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.ModEq.comm`",
      "where": "mathlib4 commit c5ea00351c28e24afc9f0f84379aa41082b1188f (v4.30.0)",
      "who": "the Mathlib contributors",
      "year": 2026
    }
  ],
  "source": "statement-only extraction of `Nat.ModEq.comm` from Mathlib v4.30.0; no proof value was exposed"
}