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Proof step 12 from proof lf-valid-recs-valid-peb (previous step)

# apebs = # wlar, wlar[n0] = wl-entry(m1, used), apebs[n0] = mkpeb(aehdr, avhdr, buf, m, boolvar), recs[avhdr.vol × avhdr.leb] = recovery-entry(n0, n1), n0 < m0, n0 < # wlar, valid-wl(subarray(apebs, 0, m0), subarray(wlar, 0, m0)), avhdr.vol × avhdr.leb ∈ recs, m0 ≤ # wlar ⊦ valid-peb(avhdr.vol, avhdr.leb, mkpeb(aehdr, avhdr, buf, m, boolvar))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ valid-wl(apebs, wlar) ↔ (∀ n. n < # wlar → (wlar[n].status = erroneous ↔ apebs[n].bad) ∧ (wlar[n].status = free → apebs[n].vidhdr = empty) ∧ (wlar[n].status ≠ erroneous ∧ wlar[n].status ≠ erasing → apebs[n].echdr = aechdr(wlar[n].ec)) ∧ (wlar[n].status = used → (∃ v, m. valid-peb(v, m, apebs[n]) ∧ apebs[n].vidhdr.sqn = valid-sqns(v, m, apebs).max)))
Proof step 14:
# apebs = # wlar, recs[avhdr.vol × avhdr.leb] = recovery-entry(n0, n1), apebs[n0] = mkpeb(aehdr, avhdr, buf, m, boolvar), wlar[n0] = wl-entry(m1, used), n0 < # wlar, n0 < m0, avhdr.vol × avhdr.leb ∈ recs, m0 ≤ # wlar, ∀ n. n < # subarray(wlar, 0, m0) → (subarray(wlar, 0, m0)[n].status = erroneous ↔ subarray(apebs, 0, m0)[n].bad) ∧ (subarray(wlar, 0, m0)[n].status = free → subarray(apebs, 0, m0)[n].vidhdr = empty) ∧ ( subarray(wlar, 0, m0)[n].status ≠ erroneous ∧ subarray(wlar, 0, m0)[n].status ≠ erasing → subarray(apebs, 0, m0)[n].echdr = aechdr(subarray(wlar, 0, m0)[n].ec)) ∧ ( subarray(wlar, 0, m0)[n].status = used → (∃ v, m. valid-peb(v, m, subarray(apebs, 0, m0)[n]) ∧ subarray(apebs, 0, m0)[n].vidhdr.sqn = valid-sqns(v, m, subarray(apebs, 0, m0)).max)) ⊦ valid-peb(avhdr.vol, avhdr.leb, mkpeb(aehdr, avhdr, buf, m, boolvar))

Rule argument

spec: ubi-base name: valid-wl seq: ⊦ valid-wl(apebs, wlar) ↔ (∀ n. n < # wlar → (wlar[n].status = erroneous ↔ apebs[n].bad) ∧ (wlar[n].status = free → apebs[n].vidhdr = empty) ∧ ( wlar[n].status ≠ erroneous ∧ wlar[n].status ≠ erasing → apebs[n].echdr = aechdr(wlar[n].ec)) ∧ ( wlar[n].status = used → (∃ v, m. valid-peb(v, m, apebs[n]) ∧ apebs[n].vidhdr.sqn = valid-sqns(v, m, apebs).max))) subst: [wlar, apebs] → [subarray(wlar, 0, m0), subarray(apebs, 0, m0)] flags: <all paths>

Additional information

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