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Proof step 8 from proof lf-valid-wl-free-emptyvidhdr (previous step)

wlar[n] = wl-entry(m, free), apebs[n] = mkpeb(aehdr, avhdr, buf, m0, false), n < # wlar, n < # apebs, ubi-io-inv(apebs), ubi-io-peb-inv(mkpeb(aehdr, avhdr, buf, m0, false)), 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)) ⊦ avhdr = empty ∧ aehdr.valid? ∧ m0 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
apebs[n] = mkpeb(aechdr(m), empty, buf, m0, false), wlar[n] = wl-entry(m, free), n < # apebs, n < # wlar, ubi-io-inv(apebs), ubi-io-peb-inv(mkpeb(aechdr(m), empty, buf, m0, false)) ⊦ m0 = 0

Rule argument

Additional information

Used simplifier rules: ubi-io-inv-fwd: n < # apebs ⊦ apebs[n] = apeb ∧ ubi-io-inv(apebs) → ubi-io-peb-inv(apeb);% ⊦ m < n → (n ≤ m ↔ false); (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ aechdr(m).valid?; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).vidhdr = avhdr; (s)% ⊦ wl-entry(m, stat).ec = m; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).echdr = aehdr; (s)% ⊦ free ≠ erasing; (s)% ⊦ used ≠ free; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).bad ↔ boolvar; (s)% ⊦ free ≠ erroneous; (s)% ⊦ wl-entry(m, stat).status = stat; (s)