Mathlib v4.30 source proposition Nat.descFactorial_one

Identifier: F:ml430-nat-descfactorial-one-d4856d4a
Proof route: kernel-lean
External status: proved
Axiom footprint: Empty

Recorded description

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

Formal statement

∀ (n : ℕ), n.descFactorial 1 = n

Dependencies

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1 direct dependencies 0 direct dependents

Evidence

autogenesis-operation-13843f88b89e9a23

Kind: kernel-term
Status: checked

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

Checker command

python3 scripts/check-autogenesis-bounded-induction-family.py

Evidence notes

Derived from an independently replayed bounded-induction receipt. The registered fact-operation checker (scripts/check-autogenesis-bounded-induction-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 first fact this producer closes that bare reflexivity could not (docs/autogenesis/229-nat-descfactorial-one-reflexivity-decline.md); the operation that settles it also independently re-derives axiom-free kernel proofs of two other facts already proved through a separate, narrower operation (see artifacts/autogenesis/mathlib-bounded-induction-family-ascfactorial-zero-v1.json and mathlib-bounded-induction-family-descfactorial-zero-v1.json), which is the evidence of generality this operation is registered for.

Provenance

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