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:34316

Content

What VA contributes. Proofs reduce ambiguity and eliminate many LA burdens 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 artifact 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.