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Proof step 14 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, m0 < m → (wlar[m0].status = erroneous ↔ apebs[m0].bad) ∧ (wlar[m0].status = free → apebs[m0].vidhdr = empty) ∧ (wlar[m0].status ≠ erroneous ∧ wlar[m0].status ≠ erasing → apebs[m0].echdr = aechdr(wlar[m0].ec)) ∧ (wlar[m0].status = used → (∃ v, m4. valid-peb(v, m4, apebs[m0]) ∧ apebs[m0].vidhdr.sqn = valid-sqns(v, m4, apebs, m).max)) ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
# wlar = # apebs, avhdr.sqn = ∅.max, wlar[m0] = wl-entry(m3, used), recs[v × m4] = recovery-entry(m0, m1), apebs[m0] = mkpeb(aechdr(m3), avhdr, buf, m2, false), valid-sqns(v, m4, apebs, m) = ∅, m0 + 1 < # apebs, m0 < # apebs, m < # apebs, m0 < m, valid-peb(v, m4, mkpeb(aechdr(m3), avhdr, buf, m2, false)), v × m4 ∈ recs ⊦

Rule argument

Additional information

Used simplifier rules: ⊦ used ≠ free; (s)% ⊦ wl-entry(m, stat).ec = m; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).echdr = aehdr; (s)% ⊦ used ≠ erasing; (s)%⊦ valid-peb(v, m, mkpeb(aehdr, avhdr, buf, m0, boolvar)) → avhdr.leb = m; (s)%⊦ valid-peb(v, m, mkpeb(aehdr, avhdr, buf, m0, boolvar)) → avhdr.vol = v; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).vidhdr = avhdr; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).bad ↔ boolvar; (s)% ⊦ used ≠ erroneous; (s)% ⊦ wl-entry(m, stat).status = stat; (s)