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Proof step 30 from proof valid-wl-use (previous step)

# apebs = # wlar, wlar[n0] = wl-entry(m3, stat), apebs[n0] = mkpeb(aehdr1, avhdr1, buf1, m2, boolvar1), n0 < # wlar, n < # wlar, valid-peb(mkpeb(aehdr, avhdr, buf, m0, boolvar)), valid-sqns(avhdr.vol, avhdr.leb, apebs) ≠ ∅ → valid-sqns(avhdr.vol, avhdr.leb, apebs).max < avhdr.sqn, n0 < # wlar → (wlar[n0].status = erroneous ↔ apebs[n0].bad) ∧ (wlar[n0].status = free → apebs[n0].vidhdr = empty) ∧ (wlar[n0].status ≠ erroneous ∧ wlar[n0].status ≠ erasing → apebs[n0].echdr = aechdr(wlar[n0].ec)) ∧ (wlar[n0].status = used → (∃ v, m. valid-peb(v, m, apebs[n0]) ∧ apebs[n0].vidhdr.sqn = valid-sqns(v, m, apebs).max)), ∀ m. m < # wlar ∧ m ≠ n ∧ wlar[m].status = used → apebs[m].vidhdr.vol ≠ avhdr.vol ∨ apebs[m].vidhdr.leb ≠ avhdr.leb ⊦ n0 = n, (stat = erroneous ↔ boolvar1) ∧ (stat = free → avhdr1 = empty) ∧ (stat ≠ erroneous ∧ stat ≠ erasing → aehdr1 = aechdr(m3)) ∧ ( stat = used → (∃ v, m. valid-peb(v, m, mkpeb(aehdr1, avhdr1, buf1, m2, false)) ∧ avhdr1.sqn = valid-sqns(v, m, apebs[n, mkpeb(aehdr, avhdr, buf, m0, boolvar)]).max))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 31:
# apebs = # wlar, avhdr1.sqn = valid-sqns(v, m, apebs).max, apebs[n0] = mkpeb(aechdr(m3), avhdr1, buf1, m2, false), wlar[n0] = wl-entry(m3, used), n < # wlar, n0 < # wlar, valid-peb(mkpeb(aehdr, avhdr, buf, m0, boolvar)), valid-peb(v, m, mkpeb(aechdr(m3), avhdr1, buf1, m2, false)), valid-sqns(avhdr.vol, avhdr.leb, apebs) ≠ ∅ → valid-sqns(avhdr.vol, avhdr.leb, apebs).max < avhdr.sqn, ∀ m. m < # wlar ∧ m ≠ n ∧ wlar[m].status = used → apebs[m].vidhdr.vol ≠ avhdr.vol ∨ apebs[m].vidhdr.leb ≠ avhdr.leb ⊦ avhdr1.sqn = valid-sqns(v, m, apebs[n, mkpeb(aehdr, avhdr, buf, m0, boolvar)]).max, n0 = n

Rule argument

Additional information

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