Mathlib v4.30 source proposition Nat.fib_strictMonoOn

Identifier: F:ml430-nat-fib-strictmonoon-905810a9
Proof route: kernel-lean
External status: proved
Axiom footprint: Empty

Recorded description

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

Formal statement

StrictMonoOn Nat.fib (Set.Ici 2)

Dependencies

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

7 direct dependencies 1 direct dependents

Evidence

kernel-Nat.fib_strictmonoOn

Kind: kernel-term
Status: checked

Supports: StrictMonoOn Nat.fib (Set.Ici 2)

Checker command

test "$(cargo run -q -p axeyum-lean-kernel --release --example nat_theorem_inventory -- fib_strictmonoOn 2>/dev/null | grep -xFc 'Nat.fib_strictmonoOn	5	((x0 : AxNat) -> ((x1 : AxNat) -> ((x2 : AxNat.le (AxNat.succ (AxNat.succ AxNat.zero)) x0) -> ((x3 : AxNat.le (AxNat.succ (AxNat.succ AxNat.zero)) x1) -> ((x4 : AxNat.lt x0 x1) -> AxNat.lt (AxNat.fib x0) (AxNat.fib x1))))))')" -ge 1

Evidence notes

The kernel re-infers the theorem type from the constructed term. `Set.Ici 2` is unwound to two explicit `Le 2` hypotheses (`succ (succ zero)` for the literal `2`), matching Mathlib's `StrictMonoOn Nat.fib (Set.Ici 2)` unfolded to `forall a b, 2 <= a -> 2 <= b -> a < b -> fib a < fib b`. Proved from fib_add_two_strictmono by peeling two succs off each bound (two applications of pos_implies_succ_pred per side) and transporting back.

footprint-Nat.fib_strictmonoOn

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_strictmonoOn 2>/dev/null | grep -xFc $'nat\tNat.fib_strictmonoOn\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_strictMonoOn` from Mathlib v4.30.0; no proof value was exposed",
  "prior_art": [
    {
      "who": "the Mathlib contributors",
      "what": "the theorem declaration `Nat.fib_strictMonoOn`",
      "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"
    }
  ]
}