Mathlib v4.30 source proposition Nat.fib_lt_fib

Identifier: F:ml430-nat-fib-lt-fib-3582b881
Proof route: kernel-lean
External status: proved
Axiom footprint: Empty

Recorded description

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

Formal statement

∀ {m : ℕ}, 2 ≤ m → ∀ {n : ℕ}, Nat.fib m < Nat.fib n ↔ m < n

Dependencies

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6 direct dependencies 1 direct dependents

Evidence

kernel-Nat.fib_lt_fib

Kind: kernel-term
Status: checked

Supports: 2 <= m -> (Nat.fib m < Nat.fib n <-> m < n)

Checker command

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

Evidence notes

The kernel re-infers the theorem type from the constructed term, matching Mathlib's `2 <= m -> (fib m < fib n <-> m < n)` (the `n`-quantifier is moved after the hypothesis rather than before it, since `Le 2 m` does not mention `n`; content-identical, not syntax-identical, matching this ledger's stated convention). Reverse direction is fib_strictmonoOn (needing Le 2 n, derived from Le 2 m and the weakened Lt m n by transitivity); forward direction is the contrapositive via lt_or_ge, fib_mono, lt_of_lt_of_le and lt_irrefl.

footprint-Nat.fib_lt_fib

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