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Proof step 12 from proof valid-recs-in-nonempty-sqns (previous step)

# 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)) ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
# 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, avhdr.vol × avhdr.leb ∈ recs, ∀ n. n < m → (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, m4. valid-peb(v, m4, apebs[n]) ∧ apebs[n].vidhdr.sqn = valid-sqns(v, m4, apebs, m).max)) ⊦

Rule argument

Additional information

Used simplifier rules: n ≤ # apebs ⊦ valid-sqns(v, m, subarray(apebs, 0, n)) = valid-sqns(v, m, apebs, n); (s)% ⊦ m < n → m ≤ n; (s)% ⊦ n0 < n → subarray(apebs, m, n)[n0] = apebs[m + n0]; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n + 0 = n; (s)% ⊦ n0 < n → subarray(wlar, m, n)[n0] = wlar[m + n0]; (s)% ⊦ # subarray(wlar, m, n) = n; (s)