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Proof step 33 from proof valid-wl-write-unmapped (previous step)

# apebs = # wlar, avhdr1.sqn = valid-sqns(VTBL_VOLID, VTBL_LNUM, apebs).max, avhdr0.sqn = valid-sqns(v, m, apebs).max, apebs[n0] = mkpeb(aechdr(m6), avhdr1, buf1, m2, false), apebs[n] = mkpeb(aehdr0, avhdr2, buf2, m3, boolvar0), apebs[n1] = mkpeb(aechdr(m4), avhdr0, buf0, m1, false), wlar[n0] = wl-entry(m6, used), wlar[n] = wl-entry(m5, erasing), wlar[n1] = wl-entry(m4, used), vols[v][m] = unmapped, mkpeb(aechdr(m6), avhdr1, buf1, m2, false).echdr.valid?, n0 < # wlar, n1 < # wlar, n < # wlar, m < # vols[v], is-encoded(to-vtbl(vols), buf1), valid-peb(v, m, mkpeb(aehdr, avhdr, buf, m0, boolvar)), valid-peb(v, m, mkpeb(aehdr0, avhdr2, buf2, m3, boolvar0)), valid-peb(mkpeb(aehdr, avhdr, buf, m0, boolvar)), valid-peb(v, m, mkpeb(aechdr(m4), avhdr0, buf0, m1, false)), v ∈ 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, ∃ m0, m1, m3. mkpeb(aechdr(m6), avhdr1, buf1, m2, false).vidhdr = avidhdr(VTBL_VOLID, VTBL_LNUM, m0, m1, m3) ∧ (m1 ≠ 0 → m1 ≤ datasize(mkpeb(aechdr(m6), avhdr1, buf1, m2, false).data) ∧ m3 = checksum(mkpeb(aechdr(m6), avhdr1, buf1, m2, false).data, m1)) ⊦ avhdr0.sqn = ((valid-sqns(v, m, apebs) -- avhdr2.sqn) ++ avhdr.sqn).max, n1 = n, mkpeb(aechdr(m6), avhdr1, buf1, m2, false).bad, VTBL_VOLID ∈ vols

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 34:
# apebs = # wlar, avhdr0.sqn = valid-sqns(v, m, apebs).max, vols[v][m] = unmapped, wlar[n1] = wl-entry(m4, used), wlar[n] = wl-entry(m5, erasing), wlar[n0] = wl-entry(m6, used), apebs[n1] = mkpeb(aechdr(m4), avhdr0, buf0, m1, false), apebs[n] = mkpeb(aehdr0, avhdr2, buf2, m3, boolvar0), apebs[n0] = mkpeb(aechdr(m6), avidhdr(VTBL_VOLID, VTBL_LNUM, valid-sqns(VTBL_VOLID, VTBL_LNUM, apebs).max, m8, m7), buf1, m2, false), m < # vols[v], n < # wlar, n1 < # wlar, n0 < # wlar, is-encoded(to-vtbl(vols), buf1), valid-peb(v, m, mkpeb(aechdr(m4), avhdr0, buf0, m1, false)), valid-peb(mkpeb(aehdr, avhdr, buf, m0, boolvar)), valid-peb(v, m, mkpeb(aehdr0, avhdr2, buf2, m3, boolvar0)), valid-peb(v, m, mkpeb(aehdr, avhdr, buf, m0, boolvar)), v ∈ vols, m8 ≠ 0 → m8 ≤ datasize(buf1) ∧ m7 = checksum(buf1, m8), ∀ 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 ⊦ avhdr0.sqn = ((valid-sqns(v, m, apebs) -- avhdr2.sqn) ++ avhdr.sqn).max, n1 = n, VTBL_VOLID ∈ vols

Rule argument

Additional information

Used simplifier rules: ⊦ avidhdr(v, m, m0, m1, m2).sqn = m0; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).data = buf; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).bad ↔ boolvar; (s)% ⊦ aechdr(m).valid?; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).echdr = aehdr; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).vidhdr = avhdr; (s)