Mathlib v4.30 source proposition Nat.bit_false

Identifier: F:ml430-nat-bit-false-98b0bf2a
Proof route: kernel-lean
External status: proved
Axiom footprint: Empty

Recorded description

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

Formal statement

Nat.bit false = fun x => 2 * x

Dependencies

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0 direct dependencies 0 direct dependents

Evidence

autogenesis-operation-nat-bit-constructor-bit-false

Kind: kernel-term
Status: checked

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

Checker command

python3 scripts/check-autogenesis-nat-bit-constructor-family.py

Evidence notes

Derived from a proof-isolated statement import of the pinned Mathlib v4.30.0 declaration `Nat.bit_false` (statement only -- `import_statement_ndjson` refuses any proof-bearing or trusted declaration, and the import admitted 60 declarations with 0 axioms), handed to the target-agnostic producer `axeyum_lean_import::producers::bounded_induction::propose_bounded_induction`. No proof code was written for this fact: the same producer, unchanged, closed three sibling facts of this family in the same run and declined six others with typed reasons. The registered checker (scripts/check-autogenesis-nat-bit-constructor-family.py) replays every accept from the hash-pinned export through a fresh independent kernel, requires every receipt field to match this row, re-runs the six declines and requires them to still decline, and re-runs an outcome-blind FALSE mutation control and requires it to be refused.

Provenance

{
  "date": "2026-08-29",
  "established_by": "not established in this ledger",
  "source": "statement-only extraction of `Nat.bit_false` from Mathlib v4.30.0; no proof value was exposed",
  "prior_art": [
    {
      "who": "the Mathlib contributors",
      "what": "the theorem declaration `Nat.bit_false`",
      "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"
    }
  ]
}