Mathlib v4.30 source proposition Int.fib_zero

Identifier: F:ml430-int-fib-zero-439bfeee
Proof route: kernel-lean
External status: proved
Axiom footprint: Empty

Recorded description

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

Formal statement

Int.fib 0 = 0

Dependencies

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0 direct dependencies 0 direct dependents

Evidence

kernel-Int.fib_zero

Kind: kernel-term
Status: checked

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

Checker command

test "$(cargo run -q --release -p axeyum-lean-kernel --example int_theorem_inventory 2>/dev/null | grep -c '^theorem[[:space:]]Int\.fib_zero[[:space:]]')" -eq 1

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_zero

Kind: exhaustive-enumeration
Status: checked

Supports: axiom_footprint: [] -- the integer prelude's trusted surface is empty, which bounds this theorem

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 this theorem. --release is MANDATORY here.

coverage-Int.fib_zero

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": "2026-09-01",
  "established_by": "axeyum-lean-kernel build_int_prelude (crates/axeyum-lean-kernel/src/int_prelude/fibonacci.rs)",
  "source": "statement-only extraction of `Int.fib_zero` from Mathlib v4.30.0; no proof value was exposed",
  "prior_art": [
    {
      "who": "the Mathlib contributors",
      "what": "the theorem declaration `Int.fib_zero`",
      "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"
    }
  ]
}