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Proof step 14 from proof lf-valid-recs-valid-peb (previous step)

# 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))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
# 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, avhdr.vol × avhdr.leb ∈ recs, m0 ≤ # wlar, ∀ n. n < m0 → (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, m2. valid-peb(v, m2, apebs[n]) ∧ apebs[n].vidhdr.sqn = valid-sqns(v, m2, apebs, m0).max)) ⊦ valid-peb(avhdr.vol, avhdr.leb, mkpeb(aehdr, avhdr, buf, m, boolvar))

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 → (n < m ↔ false); (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ 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)