FPF Reference

    C.3.A:B.4 VA lane — proofs that match the kind [A/I]

    Preface node heading:c-3-a-b-4-va-lane-proofs-that-match-the-kind-a-i:39642

    What this page is

    This is generated FPF reference text from the specification preface or supporting sections. It helps interpret FPF; it is not FPF Reference product documentation.

    Methodology

    Use it to understand how the specification wants to be read, then return to a route, pattern, or work packet for active work. Cite generated IDs only when the wording changes the task decision.

    Content

    What VA contributes. Proofs reduce ambiguity and eliminate many LA proof requirements when they truly quantify over the intended kind and live in the declared Scope.

    VA‑patterns (informative):

    • Proof over the Kind (F7–F8). “For every PassengerCar, the property holds” (notation hint: ∀x:PassengerCar). If the property depends on subkind‑specific rules, split lemmas per subkind.
    • Proof‑carrying components. When the content is F8 (dependent types), the build rejects violations; LA can shrink to conformance smoke within the slices.
    • Up‑to‑iso (AT K3). Equational reasoning “up‑to‑iso” is acceptable only if the KindSignature works at that level and receivers accept KindBridge that preserves equivalences.

    VA‑obligations (normative):

    • VA‑1. A proof carrier SHALL cite the Kind it quantifies over and reference the Claim scope slices it assumes.
    • VA‑2. Cross‑context acceptance of proofs SHALL use both bridges (Scope+Kind) and apply Φ/Ψ penalties to R (never to F/G).
    • VA‑3. If the proof relies on tool kernels, their TA status SHALL be disclosed; weakening TA MUST NOT be “paid for” by silent scope widening.

    Mini‑example (VA). Policy P: “∀ x: PassengerCar. stoppingDistance(x) ≤ 50 m on dry at speed≤50.” — Kind: PassengerCar ⊑ Vehicle (K2), signature F4 (predicates). — Scope: {surface=dry, speed≤50, rig=v3, Γ_time=rolling 180 d}. — Proof: a proof assistant lemma over PassengerCar (tool choice is context‑local). — Reuse to Plant‑B: a Scope Bridge with CL=2 (rig bias) and a KindBridge with CL^k=3 (same classification). Apply the scope‑bridge penalty for CL=2 and the kind‑bridge penalty for CL^k=3 to R.

    Last Updated: 2026-06-08 — upstream FPF commit 093d30e8 (github.com/ailev/FPF)