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Proof step 19 from proof valid-wl-map (previous step)

# apebs = # wlar, avhdr1.leb = VTBL_LNUM, avhdr2.leb = avhdr.leb, avhdr1.vol = VTBL_VOLID, avhdr2.vol = avhdr.vol, wlar[n0] = wl-entry(m8, used), wlar[m] = wl-entry(m7, used), apebs[n1] = mkpeb(aehdr3, avhdr3, buf3, m5, boolvar3), apebs[n, mkpeb(aehdr, avhdr, buf, m1, boolvar)][n1] = mkpeb(aehdr0, avhdr0, buf0, m2, boolvar0), vols[avhdr.vol][avhdr.leb] = unmapped, apebs[n0] = mkpeb(aehdr1, avhdr1, buf1, m3, boolvar1), apebs[m] = mkpeb(aehdr2, avhdr2, buf2, m4, boolvar2), wlar[n, wl-entry(aehdr.ec, used)][n1] = wl-entry(m6, stat), avhdr.leb < # vols[avhdr.vol], n < # wlar, n0 < # wlar, n1 < # wlar, m < # wlar, is-encoded(to-vtbl(vols), buf1), valid-peb(mkpeb(aehdr, avhdr, buf, m1, boolvar)), avhdr.vol ∈ vols, valid-sqns(avhdr.vol, avhdr.leb, apebs) ≠ ∅ → valid-sqns(avhdr.vol, avhdr.leb, apebs).max < avhdr.sqn, ∀ v, m0, n2. vols[v][m0] = ⌜n2⌝ ∧ v ∈ vols ∧ m0 < # vols[v] ↔ wlar[n2].status = used ∧ n2 < # wlar ∧ apebs[n2].vidhdr.valid? ∧ apebs[n2].vidhdr.vol = v ∧ apebs[n2].vidhdr.leb = m0 ∧ 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)) ⊦ m = n, VTBL_VOLID ∈ vols, (stat = erroneous ↔ boolvar0) ∧ (stat = free → avhdr3 = empty) ∧ (stat ≠ erroneous ∧ stat ≠ erasing → aehdr0 = aechdr(m6)) ∧ ( stat = used → (∃ v, m0. valid-peb(v, m0, mkpeb(aehdr0, avhdr0, buf0, m2, false)) ∧ avhdr0.sqn = valid-sqns(v, m0, apebs[n, mkpeb(aehdr, avhdr, buf, m1, boolvar)]).max))

User applied rule all left

And obtained the following new goals

Proof step 20:
# apebs = # wlar, avhdr2.leb = avhdr.leb, avhdr1.leb = VTBL_LNUM, avhdr2.vol = avhdr.vol, avhdr1.vol = VTBL_VOLID, vols[avhdr2.vol][avhdr2.leb] = ⌜m⌝ ∧ avhdr2.vol ∈ vols ∧ avhdr2.leb < # vols[avhdr2.vol] ↔ wlar[m].status = used ∧ m < # wlar ∧ apebs[m].vidhdr.valid? ∧ apebs[m].vidhdr.vol = avhdr2.vol ∧ apebs[m].vidhdr.leb = avhdr2.leb ∧ m ≠ n0, wlar[n, wl-entry(aehdr.ec, used)][n1] = wl-entry(m6, stat), apebs[m] = mkpeb(aehdr2, avhdr2, buf2, m4, boolvar2), apebs[n0] = mkpeb(aehdr1, avhdr1, buf1, m3, boolvar1), vols[avhdr.vol][avhdr.leb] = unmapped, apebs[n, mkpeb(aehdr, avhdr, buf, m1, boolvar)][n1] = mkpeb(aehdr0, avhdr0, buf0, m2, boolvar0), apebs[n1] = mkpeb(aehdr3, avhdr3, buf3, m5, boolvar3), wlar[m] = wl-entry(m7, used), wlar[n0] = wl-entry(m8, used), m < # wlar, n1 < # wlar, n0 < # wlar, n < # wlar, avhdr.leb < # vols[avhdr.vol], is-encoded(to-vtbl(vols), buf1), valid-peb(mkpeb(aehdr, avhdr, buf, m1, boolvar)), avhdr.vol ∈ vols, valid-sqns(avhdr.vol, avhdr.leb, apebs) ≠ ∅ → valid-sqns(avhdr.vol, avhdr.leb, apebs).max < avhdr.sqn, ∀ 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)) ⊦ m = n, VTBL_VOLID ∈ vols, (stat = erroneous ↔ boolvar0) ∧ (stat = free → avhdr3 = empty) ∧ (stat ≠ erroneous ∧ stat ≠ erasing → aehdr0 = aechdr(m6)) ∧ ( stat = used → (∃ v, m0. valid-peb(v, m0, mkpeb(aehdr0, avhdr0, buf0, m2, false)) ∧ avhdr0.sqn = valid-sqns(v, m0, apebs[n, mkpeb(aehdr, avhdr, buf, m1, boolvar)]).max))

Rule argument

pos: left 23 terms: avhdr2.vol, avhdr2.leb, m abort: F discard: T computed: T

Additional information

Used terms: avhdr2.vol, avhdr2.leb, m