Mathlib v4.30 source proposition Nat.zero_ascFactorial

Identifier: F:ml430-nat-zero-ascfactorial-af4fcdca
Proof route: kernel-lean
External status: proved
Axiom footprint: Empty

Recorded description

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

Formal statement

∀ (k : ℕ), Nat.ascFactorial 0 k.succ = 0

Dependencies

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0 direct dependencies 0 direct dependents

Evidence

autogenesis-operation-92d918ef678f3e2a

Kind: kernel-term
Status: checked

Supports: The proposition declared as `Nat.zero_ascFactorial` 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 operation was extended from three targets to five to independently re-derive an axiom-free kernel proof of `Nat.zero_ascFactorial` (`∀ (k : ℕ), Nat.ascFactorial 0 k.succ = 0`), alongside the other four facts it covers -- the second and third facts this family operation directly settles, which is further evidence of the generality this operation is registered for.

Provenance

{
  "date": "2026-08-18",
  "established_by": "not established in this ledger",
  "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.zero_ascFactorial`",
      "where": "mathlib4 commit c5ea00351c28e24afc9f0f84379aa41082b1188f (v4.30.0)",
      "who": "the Mathlib contributors",
      "year": 2026
    }
  ],
  "source": "statement-only extraction of `Nat.zero_ascFactorial` from Mathlib v4.30.0; no proof value was exposed"
}