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Proof step 21 from proof valid-wl-write-unmapped (previous step)

# apebs = # wlar, avhdr1.sqn = valid-sqns(VTBL_VOLID, VTBL_LNUM, apebs).max, 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(aechdr(m6), avhdr1, buf1, m2, false), 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)), valid-peb(VTBL_VOLID, VTBL_LNUM, mkpeb(aechdr(m6), avhdr1, buf1, m2, false)), avhdr.vol ∈ vols, n1 < # wlar → (wlar[n1].status = erroneous ↔ apebs[n1].bad) ∧ (wlar[n1].status = free → apebs[n1].vidhdr = empty) ∧ (wlar[n1].status ≠ erroneous ∧ wlar[n1].status ≠ erasing → apebs[n1].echdr = aechdr(wlar[n1].ec)) ∧ (wlar[n1].status = used → (∃ v, m. valid-peb(v, m, apebs[n1]) ∧ apebs[n1].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))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 22:
# apebs = # wlar, avhdr1.sqn = valid-sqns(VTBL_VOLID, VTBL_LNUM, apebs).max, avhdr0.sqn = valid-sqns(v, m, apebs).max, 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[avhdr.vol][avhdr.leb] = unmapped, apebs[n0] = mkpeb(aechdr(m6), avhdr1, buf1, m2, false), n < # wlar, avhdr.leb < # vols[avhdr.vol], n0 < # wlar, n1 < # wlar, is-encoded(to-vtbl(vols), buf1), valid-peb(VTBL_VOLID, VTBL_LNUM, mkpeb(aechdr(m6), avhdr1, buf1, m2, false)), valid-peb(mkpeb(aehdr, avhdr, buf, m0, boolvar)), valid-peb(v, m, mkpeb(aechdr(m4), avhdr0, buf0, m1, false)), 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 ⊦ avhdr0.sqn = valid-sqns(v, m, apebs[n, mkpeb(aehdr, avhdr, buf, m0, boolvar)]).max, n1 = n, VTBL_VOLID ∈ vols

Rule argument

Additional information

Used simplifier rules: ⊦ used ≠ erasing; (s)%⊦ valid-peb(v0, m0, apeb) → (valid-peb(v1, m1, apeb) ↔ v0 = v1 ∧ m0 = m1); (s)% ⊦ used ≠ free; (s)% ⊦ used ≠ erroneous; (s)% ⊦ wl-entry(m, stat).ec = m; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).echdr = aehdr; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).vidhdr = avhdr; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).bad ↔ boolvar; (s)% ⊦ wl-entry(m, stat).status = stat; (s)