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Proof step 18 from proof valid-wl-write-unmapped (previous step)

# apebs = # wlar, avhdr1.leb = VTBL_LNUM, avhdr1.vol = VTBL_VOLID, vols[avhdr.vol][avhdr.leb] = unmapped, apebs[n0] = mkpeb(aehdr1, avhdr1, buf1, m2, boolvar1), apebs[n1] = mkpeb(aehdr0, avhdr0, buf0, m1, boolvar0), wlar[n0] = wl-entry(m6, used), wlar[n] = wl-entry(m5, erasing), wlar[n1] = wl-entry(m4, stat), n < # wlar, avhdr.leb < # vols[avhdr.vol], n0 < # wlar, n1 < # wlar, is-encoded(to-vtbl(vols), buf1), valid-peb(mkpeb(aehdr, avhdr, buf, m0, boolvar)), avhdr.vol ∈ vols, ∀ v, m, n2. vols[v][m] = ⌜n2⌝ ∧ v ∈ vols ∧ m < # vols[v] ↔ wlar[n2].status = used ∧ n2 < # wlar ∧ apebs[n2].vidhdr.valid? ∧ apebs[n2].vidhdr.vol = v ∧ apebs[n2].vidhdr.leb = m ∧ n2 ≠ n0, ∀ 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)) ⊦ n1 = n, VTBL_VOLID ∈ vols, (stat = erroneous ↔ boolvar0) ∧ (stat = free → avhdr0 = empty) ∧ (stat ≠ erroneous ∧ stat ≠ erasing → aehdr0 = aechdr(m4)) ∧ ( stat = used → (∃ v, m. valid-peb(v, m, mkpeb(aehdr0, avhdr0, buf0, m1, false)) ∧ avhdr0.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 19:
# apebs = # wlar, avhdr1.leb = VTBL_LNUM, avhdr1.vol = VTBL_VOLID, wlar[n1] = wl-entry(m4, stat), wlar[n] = wl-entry(m5, erasing), wlar[n0] = wl-entry(m6, used), apebs[n1] = mkpeb(aehdr0, avhdr0, buf0, m1, boolvar0), apebs[n0] = mkpeb(aehdr1, avhdr1, buf1, m2, boolvar1), vols[avhdr.vol][avhdr.leb] = unmapped, n1 < # wlar, n0 < # wlar, avhdr.leb < # vols[avhdr.vol], n < # wlar, is-encoded(to-vtbl(vols), buf1), valid-peb(mkpeb(aehdr, avhdr, buf, m0, boolvar)), avhdr.vol ∈ vols, 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)), ∀ 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)), ∀ v, m, n2. vols[v][m] = ⌜n2⌝ ∧ v ∈ vols ∧ m < # vols[v] ↔ wlar[n2].status = used ∧ n2 < # wlar ∧ apebs[n2].vidhdr.valid? ∧ apebs[n2].vidhdr.vol = v ∧ apebs[n2].vidhdr.leb = m ∧ n2 ≠ n0 ⊦ n1 = n, VTBL_VOLID ∈ vols, (stat = erroneous ↔ boolvar0) ∧ (stat = free → avhdr0 = empty) ∧ (stat ≠ erroneous ∧ stat ≠ erasing → aehdr0 = aechdr(m4)) ∧ ( stat = used → (∃ v, m. valid-peb(v, m, mkpeb(aehdr0, avhdr0, buf0, m1, false)) ∧ avhdr0.sqn = valid-sqns(v, m, apebs[n, mkpeb(aehdr, avhdr, buf, m0, boolvar)]).max))

Rule argument

pos: left 18 terms: n0 abort: F discard: F computed: T

Additional information

Used terms: n0