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Proof step 5 from proof lf-valid-recs-max (previous step)

# apebs = # wlar, apebs[m0] = mkpeb(aehdr, avhdr, buf, m1, boolvar), recs[v × n] = recovery-entry(m0, avhdr.sqn), m0 < m, m0 < # wlar, valid-peb(v, n, mkpeb(aehdr, avhdr, buf, m1, boolvar)), valid-recs(subarray(apebs, 0, m), subarray(wlar, 0, m), recs), valid-recs-sqns(apebs, recs), valid-wl(subarray(apebs, 0, m), subarray(wlar, 0, m)), v × n ∈ recs, m ≤ # wlar ⊦ avhdr.sqn = valid-sqns(v, n, apebs, m).max

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ 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 7:
# apebs = # wlar, recs[v × n] = recovery-entry(m0, avhdr.sqn), apebs[m0] = mkpeb(aehdr, avhdr, buf, m1, boolvar), m0 < # wlar, m0 < m, valid-peb(v, n, mkpeb(aehdr, avhdr, buf, m1, boolvar)), valid-recs-sqns(apebs, recs), valid-wl(subarray(apebs, 0, m), subarray(wlar, 0, m)), v × n ∈ recs, m ≤ # wlar, ∀ ladr, m0. ladr ∈ recs ∧ recs[ladr].pnum = m0 ↔ subarray(wlar, 0, m)[m0].status = used ∧ m0 < # subarray(apebs, 0, m) ∧ subarray(apebs, 0, m)[m0].vidhdr.vol = ladr.vol ∧ subarray(apebs, 0, m)[m0].vidhdr.leb = ladr.leb ⊦ avhdr.sqn = valid-sqns(v, n, apebs, m).max

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, m), subarray(apebs, 0, m)] flags: <all paths>

Additional information

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