Mathlib v4.30 source proposition Nat.le_fib_self

Identifier: F:ml430-nat-le-fib-self-0cbccb4d
Proof route: kernel-lean
External status: proved
Axiom footprint: Empty

Recorded description

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

Formal statement

∀ {n : ℕ}, 5 ≤ n → n ≤ Nat.fib n

Dependencies

The graph shows direct ledger edges. Follow a node to open its artifact page.

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

Evidence

kernel-Nat.le_fib_self

Kind: kernel-term
Status: checked

Supports: 5 <= n -> n <= Nat.fib n

Checker command

test "$(cargo run -q -p axeyum-lean-kernel --release --example nat_theorem_inventory -- le_fib_self 2>/dev/null | grep -xFc 'Nat.le_fib_self	2	((x0 : AxNat) -> ((x1 : AxNat.le (AxNat.succ (AxNat.succ (AxNat.succ (AxNat.succ (AxNat.succ AxNat.zero))))) x0) -> AxNat.le x0 (AxNat.fib x0)))')" -ge 1

Evidence notes

The kernel re-infers the theorem type from the constructed term, matching Mathlib's `5 <= n -> n <= fib n` (the numeral 5 renders as five nested AxNat.succ over AxNat.zero, this kernel's unary literal convention). Proved from an unexposed index-shifted helper (pair-induction on k proving Le (5+k) (fib (5+k)), mirroring fib_add's own stmt_at k / stmt_at (succ k) device), instantiated at the hypothesis's own witness via le_dest + Exists.rec.

footprint-Nat.le_fib_self

Kind: exhaustive-enumeration
Status: checked

Supports: axiom_footprint: []

Checker command

test "$(cargo run -q -p axeyum-lean-kernel --release --example theorem_axiom_footprint -- Nat.le_fib_self 2>/dev/null | grep -xFc $'nat\tNat.le_fib_self\t0\t')" -ge 1

Evidence notes

The theorem-specific footprint command reports zero dependencies on axioms in the constructed Nat environment.

Provenance

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