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Proof step 29 from proof valid-wl-use (previous step)

# apebs = # wlar, apebs[n0] = mkpeb(aehdr1, avhdr1, buf1, m2, boolvar1), wlar[n0] = wl-entry(m3, stat), n < # wlar, n0 < # 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, ∀ m. m < # wlar ∧ m ≠ n ∧ wlar[m].status = used → apebs[m].vidhdr.vol ≠ avhdr.vol ∨ apebs[m].vidhdr.leb ≠ avhdr.leb, ∀ n. 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)) ⊦ 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))

User applied rule all left

And obtained the following new goals

Proof step 30:
# 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))

Rule argument

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

Additional information

Used terms: n0