Mathlib v4.30 source proposition Nat.land_assoc

Identifier: F:ml430-nat-land-assoc-ad4775b8
Proof route: kernel-lean
External status: proved
Axiom footprint: Empty

Recorded description

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

Formal statement

∀ (n m k : ℕ), n &&& m &&& k = n &&& (m &&& k)

Dependencies

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1 direct dependencies 1 direct dependents

Evidence

reconciliation-Nat.land_assoc

Kind: kernel-term
Status: checked

Supports: ∀ (n m k : ℕ), n &&& m &&& k = n &&& (m &&& k)

Evidence notes

Registers an independently constructed native theorem (`F:nat-land-assoc`, `Nat.land_assoc` in `nat_prelude/rec_agreement.rs`) whose proposition definitionally matches this proof-free imported goal -- Mathlib's `Nat.land` is `Nat.bitwise and`, and our `Nat.land` is proved equal to the `bitwise and_fn` specialization by `Nat.bitwise_and_eq_land`, so this closes the SAME function's associativity, not a lookalike about a different definition (the criterion this repository uses to decide when flipping an `ml430` mirror is honest: Mathlib's `def` is the same function, not merely a theorem about a different one). No Autogenesis operation produced the theorem; the route taken (`land_aux_assoc_of_fuel` via a double `Nat.div_mod_unique` reconstruction plus the outer induction's own `ih`) is NOT Mathlib's own route, which is why `depends_on` still names the still-open `F:ml430-nat-land-bit-b9ab7475` -- that edge records curriculum lineage, not a dependency this proof actually used.

Provenance

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