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Proof step 3 from proof lf-valid-recs-valid-peb (previous step)

# apebs = # wlar, recs[v × m] = recovery-entry(n0, n1), n0 < m0, n0 < # wlar, valid-recs(subarray(apebs, 0, m0), subarray(wlar, 0, m0), recs), valid-wl(subarray(apebs, 0, m0), subarray(wlar, 0, m0)), v × m ∈ recs, m0 ≤ # wlar ⊦ valid-peb(v, m, apebs[n0])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ valid-recs(apebs, wlar, recs) ↔ (∀ ladr, m. ladr ∈ recs ∧ recs[ladr].pnum = m ↔ wlar[m].status = used ∧ m < # apebs ∧ apebs[m].vidhdr.vol = ladr.vol ∧ apebs[m].vidhdr.leb = ladr.leb)
Proof step 5:
# apebs = # wlar, recs[v × m] = recovery-entry(n0, n1), n0 < # wlar, n0 < m0, valid-wl(subarray(apebs, 0, m0), subarray(wlar, 0, m0)), v × m ∈ recs, m0 ≤ # wlar, ∀ ladr, m. ladr ∈ recs ∧ recs[ladr].pnum = m ↔ subarray(wlar, 0, m0)[m].status = used ∧ m < # subarray(apebs, 0, m0) ∧ subarray(apebs, 0, m0)[m].vidhdr.vol = ladr.vol ∧ subarray(apebs, 0, m0)[m].vidhdr.leb = ladr.leb ⊦ valid-peb(v, m, apebs[n0])

Rule argument

spec: ubi-crash-recovery-base name: valid-recs seq: ⊦ valid-recs(apebs, wlar, recs) ↔ (∀ ladr, m. ladr ∈ recs ∧ recs[ladr].pnum = m ↔ wlar[m].status = used ∧ m < # apebs ∧ apebs[m].vidhdr.vol = ladr.vol ∧ apebs[m].vidhdr.leb = ladr.leb) subst: [recs, wlar, apebs] → [recs, subarray(wlar, 0, m0), subarray(apebs, 0, m0)] flags: <all paths>

Additional information

Used terms: recs, subarray(wlar, 0, m0), subarray(apebs, 0, m0)