Mathlib v4.30 source proposition Int.fib_of_odd

Identifier: F:ml430-int-fib-of-odd-66560495
Proof route: kernel-lean
External status: proved
Axiom footprint: Empty

Recorded description

The proposition declared as `Int.fib_of_odd` in the pinned Mathlib v4.30 source.

Formal statement

∀ {n : ℤ}, Odd n → Int.fib n = ↑(Nat.fib n.natAbs)

Dependencies

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10 direct dependencies 1 direct dependents Graph shows the first 8 on each side.

Evidence

kernel-Int.fib_of_odd

Kind: kernel-term
Status: checked

Supports: Int.fib_of_odd is admitted by the trusted kernel gate with the type recorded in formal.statement.

Checker command

cargo run -q --release -p axeyum-lean-kernel --example int_theorem_inventory 2>/dev/null | grep -cE '^theorem[[:space:]]Int\.fib_of_odd[[:space:]]'

Evidence notes

int_theorem_inventory lists every Declaration::Theorem in the integer prelude with its canonical type; the grep asserts the exact tab-anchored name. --release is MANDATORY: this binary also builds creal/complex/cpoint, which overflow the default debug thread stack.

footprint-Int.fib_of_odd

Kind: exhaustive-enumeration
Status: checked

Supports: axiom_footprint: [] -- the integer prelude's trusted surface is empty, which bounds Int.fib_of_odd

Checker command

cargo run -q --release -p axeyum-lean-kernel --example nat_axiom_inventory -- --include-constructed --require-axiom-free integer

Evidence notes

Re-measured on this tree: integer trusted surface = 0. That bounds every declaration in the integer environment, including Int.fib_of_odd. --release is MANDATORY here.

evaluation-Int.fib_of_odd-both-signs

Kind: witness-replay
Status: checked

Supports: fib_of_odd instantiated at a concrete odd index of EACH sign: fib 3 = 2 (Nat.fib 3 = 2, and Odd 3 witnessed by 1) and fib (negSucc 2) [= fib (-3)] = 2, reusing the SAME Nat.Odd 3 witness at the opposite constructor -- confirming the negSucc branch's sign-cancellation ((-1)^m = 1 for even m, transported from Nat.Even m's witness) actually fires, not merely that the ofNat branch's free reduction does.

Checker command

cargo test -p axeyum-lean-kernel --lib int_prelude::int_prelude_tests::fib_of_odd_applies_at_a_concrete_odd_index_of_each_sign 2>&1 | grep -c '^test result: ok\. 1 passed'

Evidence notes

crates/axeyum-lean-kernel/src/int_prelude/int_prelude_tests.rs. The suite must be run with an explicit test-name filter and a NONZERO pass count confirmed -- `cargo test --lib int_prelude::` (bare form) substring-matches into an unrelated ~148s creal_point suite per this repository's own documented gotcha.

coverage-Int.fib_of_odd

Kind: witness-replay
Status: checked

Supports: int_prelude_tests.rs's every_int_declaration_is_checked_and_axiom_free asserts, against the ENVIRONMENT rather than a hand-maintained list, that every live Int.* Definition/Theorem (this one included) is listed in derived_laws/derived_lemmas/asserted_laws/definition_names and carries an empty axiom footprint.

Checker command

cargo test -p axeyum-lean-kernel --lib int_prelude::int_prelude_tests::every_int_declaration_is_checked_and_axiom_free 2>&1 | grep -c '^test result: ok\. 1 passed'

Evidence notes

Guards against the class of gap CLAUDE.md documents repeatedly: a Definition/Theorem live in the prelude but absent from every hand-maintained list, which would otherwise receive no axiom-footprint check at all.

Provenance

{
  "date": "2026-08-28",
  "established_by": "axeyum-lean-kernel build_int_prelude (crates/axeyum-lean-kernel/src/int_prelude/fibonacci.rs, declare_fib_of_odd)",
  "source": "canonical type read via int_theorem_inventory's own output (cargo run -q --release -p axeyum-lean-kernel --example int_theorem_inventory), which prints one row per Declaration::Theorem in the integer prelude with kernel.render_lean(declaration.ty()) as the last field. That row was grepped and copied verbatim into formal.statement, replacing the earlier statement-only lean4-surface extraction.",
  "prior_art": [
    {
      "who": "the Mathlib contributors",
      "what": "the theorem declaration `Int.fib_of_odd`",
      "where": "mathlib4 commit c5ea00351c28e24afc9f0f84379aa41082b1188f (v4.30.0)",
      "year": 2026,
      "attribution": "the proposition statement was read from the pinned statement-only inventory; the proof PRODUCED here is this kernel's own construction (F:int-odd's natAbs-based Odd, plus Nat.even_iff_odd_succ, plus the Weierstrass-style pow(-1)^m=1 induction over the k+k witness shape), not a transcription of Mathlib's tactic proof, which was never consulted."
    }
  ]
}