Mathlib v4.30 source proposition Nat.fib_mono

Identifier: F:ml430-nat-fib-mono-cc6afe09
Proof route: kernel-lean
External status: proved
Axiom footprint: Empty

Recorded description

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

Formal statement

Monotone Nat.fib

Dependencies

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2 direct dependencies 1 direct dependents

Evidence

kernel-Nat.fib_mono

Kind: kernel-term
Status: checked

Supports: Monotone Nat.fib

Checker command

test "$(cargo run -q -p axeyum-lean-kernel --release --example nat_theorem_inventory -- fib_mono 2>/dev/null | grep -xFc 'Nat.fib_mono	3	((x0 : AxNat) -> ((x1 : AxNat) -> ((x2 : AxNat.le x0 x1) -> AxNat.le (AxNat.fib x0) (AxNat.fib x1))))')" -ge 1

Evidence notes

The kernel re-infers the theorem type from the constructed term. Lean's `Monotone Nat.fib` unfolds to `forall a b, a <= b -> fib a <= fib b`, exactly the rendered core proposition checked here. The proof specializes the target-agnostic `Nat.monotone_of_le_succ` combinator with the already admitted `Nat.fib_le_succ`; the kernel-observed dependency closure, not this note, is authoritative.

footprint-Nat.fib_mono

Kind: exhaustive-enumeration
Status: checked

Supports: axiom_footprint: []

Checker command

test "$(cargo run -q -p axeyum-lean-kernel --release --example theorem_axiom_footprint -- Nat.fib_mono 2>/dev/null | grep -xFc $'nat\tNat.fib_mono\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.fib_mono` from Mathlib v4.30.0; no proof value was exposed",
  "prior_art": [
    {
      "who": "the Mathlib contributors",
      "what": "the theorem declaration `Nat.fib_mono`",
      "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"
    }
  ]
}