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Proof step 15 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, 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))

User applied rule all left

And closed the goal!

Rule argument

pos: left 9 terms: n0 abort: F discard: T computed: T

Additional information

Used simplifier rules: ⊦ wl-entry(m, stat).status = stat; (s)% ⊦ used ≠ erroneous; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).bad ↔ boolvar; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).vidhdr = avhdr; (s)%⊦ valid-peb(v, m, mkpeb(aehdr, avhdr, buf, m0, boolvar)) → avhdr.vol = v; (s)%⊦ valid-peb(v, m, mkpeb(aehdr, avhdr, buf, m0, boolvar)) → avhdr.leb = m; (s)%⊦ valid-peb(v0, m0, apeb) → (valid-peb(v1, m1, apeb) ↔ v0 = v1 ∧ m0 = m1); (s) Used terms: n0