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Proof step 49 from proof valid-wl-write-unmapped (previous step)

# 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[n0] = mkpeb(aechdr(m6), avidhdr(VTBL_VOLID, VTBL_LNUM, valid-sqns(VTBL_VOLID, VTBL_LNUM, apebs).max, m7, m3), 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(aehdr, avhdr, buf, m0, boolvar)), v ∈ vols, m7 ≠ 0 → m7 ≤ datasize(buf1) ∧ m3 = checksum(buf1, m7), ∀ 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) ++ avhdr.sqn).max, n1 = n, valid-peb(v, m, apebs[n]), VTBL_VOLID ∈ vols

User applied rule all left

And obtained the following new goals

Proof step 50:
# apebs = # wlar, avhdr0.sqn = valid-sqns(v, m, apebs).max, vols[v][m] = ⌜n1⌝ ∧ v ∈ vols ∧ m < # vols[v] ↔ wlar[n1].status = used ∧ n1 < # wlar ∧ apebs[n1].vidhdr.valid? ∧ apebs[n1].vidhdr.vol = v ∧ apebs[n1].vidhdr.leb = m ∧ n1 ≠ n0, apebs[n0] = mkpeb(aechdr(m6), avidhdr(VTBL_VOLID, VTBL_LNUM, valid-sqns(VTBL_VOLID, VTBL_LNUM, apebs).max, m7, m3), buf1, m2, false), 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, 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(mkpeb(aehdr, avhdr, buf, m0, boolvar)), valid-peb(v, m, mkpeb(aechdr(m4), avhdr0, buf0, m1, false)), v ∈ vols, m7 ≠ 0 → m7 ≤ datasize(buf1) ∧ m3 = checksum(buf1, m7) ⊦ avhdr0.sqn = (valid-sqns(v, m, apebs) ++ avhdr.sqn).max, n1 = n, valid-peb(v, m, apebs[n]), VTBL_VOLID ∈ vols

Rule argument

pos: left 19 terms: v, m, n1 abort: F discard: T computed: F

Additional information

Used terms: v, m, n1