Mathlib v4.30 source proposition Nat.bitwise_swap

Identifier: F:ml430-nat-bitwise-swap-7175e90e
Proof route: kernel-lean
External status: proved
Axiom footprint: Empty

Recorded description

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

Formal statement

∀ {f : Bool → Bool → Bool}, Nat.bitwise (Function.swap f) = Function.swap (Nat.bitwise f)

Dependencies

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1 direct dependencies 1 direct dependents

Evidence

reconciliation-Nat.bitwise_swap

Kind: kernel-term
Status: checked

Supports: ∀ {f : Bool → Bool → Bool}, Nat.bitwise (Function.swap f) = Function.swap (Nat.bitwise f)

Evidence notes

Registers an independently constructed native theorem (`F:nat-bitwise-swap`, `Nat.bitwise_swap` in `nat_prelude/bitwise.rs`) whose proposition matches this proof-free imported goal up to the standard, funext-avoiding restatement this kernel uses throughout (this kernel has no `funext`, so a `Function.swap`-level function equality is stated pointwise: `forall f m n, bitwise (swap f) m n = bitwise f n m` is the applied form of `bitwise (swap f) = swap (bitwise f)`). Our `Nat.bitwise` genuinely IS Mathlib's own general combinator (not a specialization), so the flip is honest in the strongest sense this repository's mirror-flip criterion recognizes: Mathlib's `def Nat.bitwise` and ours are the same function, and this closes the same theorem about it, restated in a form this kernel can actually state.

Provenance

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