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Proof step 10 from proof valid-recs-in-nonempty-sqns (previous step)

# wlar = # apebs, wlar[m0] = wl-entry(m3, used), recs[avhdr.vol × avhdr.leb] = recovery-entry(m0, m1), apebs[m0] = mkpeb(aehdr, avhdr, buf, m2, boolvar), valid-sqns(avhdr.vol, avhdr.leb, apebs, m) = ∅, m0 + 1 < # apebs, m0 < # apebs, m < # apebs, m0 < m, valid-wl(subarray(apebs, 0, m), subarray(wlar, 0, m)), avhdr.vol × avhdr.leb ∈ recs ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ 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 12:
# wlar = # apebs, apebs[m0] = mkpeb(aehdr, avhdr, buf, m2, boolvar), recs[avhdr.vol × avhdr.leb] = recovery-entry(m0, m1), wlar[m0] = wl-entry(m3, used), valid-sqns(avhdr.vol, avhdr.leb, apebs, m) = ∅, m0 < m, m < # apebs, m0 < # apebs, m0 + 1 < # apebs, avhdr.vol × avhdr.leb ∈ recs, ∀ n. n < # subarray(wlar, 0, m) → (subarray(wlar, 0, m)[n].status = erroneous ↔ subarray(apebs, 0, m)[n].bad) ∧ (subarray(wlar, 0, m)[n].status = free → subarray(apebs, 0, m)[n].vidhdr = empty) ∧ ( subarray(wlar, 0, m)[n].status ≠ erroneous ∧ subarray(wlar, 0, m)[n].status ≠ erasing → subarray(apebs, 0, m)[n].echdr = aechdr(subarray(wlar, 0, m)[n].ec)) ∧ ( subarray(wlar, 0, m)[n].status = used → (∃ v, m0. valid-peb(v, m0, subarray(apebs, 0, m)[n]) ∧ subarray(apebs, 0, m)[n].vidhdr.sqn = valid-sqns(v, m0, subarray(apebs, 0, m)).max)) ⊦

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

Additional information

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