Mathlib v4.30 source proposition Int.ModEq.symm

Identifier: F:ml430-int-modeq-symm-984a6e67
Proof route: kernel-lean
External status: proved
Axiom footprint: Empty

Recorded description

The proposition declared as `Int.ModEq.symm` in the pinned Mathlib v4.30 source.

Formal statement

∀ {n a b : ℤ}, a ≡ b [ZMOD n] → b ≡ a [ZMOD n]

Dependencies

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

0 direct dependencies 3 direct dependents

Evidence

autogenesis-operation-modeq-4e11288764036321

Kind: kernel-term
Status: checked

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

Checker command

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

Evidence notes

Derived from an independently replayed modeq-family receipt. The registered fact-operation checker (scripts/check-autogenesis-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 the ledger's SECOND general autogenesis operation (applicability.fact_ids names four facts, not one): unfold `Int.ModEq.symm`'s definitional `ModEq n a b := a % n = b % n` and close with Eq.refl/Eq.symm/Eq.trans/Iff.intro, each reconstructed directly from Eq.rec / Iff's own constructor -- never a borrowed theorem, never a reference to the target or a sibling ModEq fact. The same producer, unmodified after being tuned only on this train family, closed all four `natural-modular-equivalence` (development) siblings blind.

Provenance

{
  "date": "2026-08-18",
  "established_by": "not established in this ledger",
  "source": "statement-only extraction of `Int.ModEq.symm` from Mathlib v4.30.0; no proof value was exposed",
  "prior_art": [
    {
      "who": "the Mathlib contributors",
      "what": "the theorem declaration `Int.ModEq.symm`",
      "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"
    }
  ]
}