Mathlib v4.30 source proposition Nat.fib_add_two_strictMono

Identifier: F:ml430-nat-fib-add-two-strictmono-c1e86d4d
Proof route: kernel-lean
External status: proved
Axiom footprint: Empty

Recorded description

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

Formal statement

StrictMono fun n => Nat.fib (n + 2)

Dependencies

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

Evidence

kernel-Nat.fib_add_two_strictmono

Kind: kernel-term
Status: checked

Supports: StrictMono (fun n => Nat.fib (n + 2))

Checker command

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

Evidence notes

The kernel re-infers the theorem type from the constructed term. `n + 2` is rendered `succ (succ n)` (defeq, and the concrete instantiation this prelude builds), matching Mathlib's `fun n => fib (n+2)` unfolded to `forall a b, a < b -> fib (a+2) < fib (b+2)`. Proved by induction mirroring perfect.rs's pow_lt_pow_of_lt, using an unconditional adjacent-step lemma (fib_add_two_lt_succ, private, from fib_add_two + fib_pos_of_pos) in place of pow's base-positivity-gated step.

footprint-Nat.fib_add_two_strictmono

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