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Proof step 3 from proof valid-wl-write-unmapped (previous step)

# apebs = # wlar, apebs[n0].vidhdr.leb = VTBL_LNUM, wlar[n0].status = used, wlar[n].status = erasing, apebs[n0].vidhdr.vol = VTBL_VOLID, vols[apeb.vidhdr.vol][apeb.vidhdr.leb] = unmapped, n1 < # wlar, n0 < # wlar, apeb.vidhdr.leb < # vols[apeb.vidhdr.vol], n < # wlar, is-encoded(to-vtbl(vols), apebs[n0].data), valid-peb(apeb), apeb.vidhdr.vol ∈ vols, ∀ 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 ⊦ VTBL_VOLID ∈ vols, (wlar[n1].status = erroneous ↔ apebs[n, apeb][n1].bad) ∧ (wlar[n1].status = free → apebs[n, apeb][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[n, apeb][n1]) ∧ apebs[n, apeb][n1].vidhdr.sqn = valid-sqns(v, m, apebs[n, apeb]).max))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 4:
# apebs = # wlar, apebs[n0].vidhdr.leb = VTBL_LNUM, wlar[n].status = erasing, wlar[n0].status = used, apebs[n0].vidhdr.vol = VTBL_VOLID, vols[avhdr.vol][avhdr.leb] = unmapped, apeb = mkpeb(aehdr, avhdr, buf, m0, boolvar), n < # wlar, avhdr.leb < # vols[avhdr.vol], n0 < # wlar, n1 < # wlar, is-encoded(to-vtbl(vols), apebs[n0].data), valid-peb(apeb), 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)) ⊦ VTBL_VOLID ∈ vols, (wlar[n1].status = erroneous ↔ apebs[n, apeb][n1].bad) ∧ (wlar[n1].status = free → apebs[n, apeb][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[n, apeb][n1]) ∧ apebs[n, apeb][n1].vidhdr.sqn = valid-sqns(v, m, apebs[n, apeb]).max))

Rule argument

spec: apeb name: elim seq: ⊦ ( ( (aehdr = apeb.echdr ∧ avhdr = apeb.vidhdr) ∧ buf = apeb.data) ∧ m = apeb.fill) ∧ (boolvar ↔ apeb.bad) ↔ apeb = mkpeb(aehdr, avhdr, buf, m, boolvar) subst: [apeb, aehdr, avhdr, buf, m, boolvar] → [apeb, aehdr, avhdr, buf, m0, boolvar]

Additional information

Used simplifier rules: ⊦ ( ((aehdr = apeb.echdr ∧ avhdr = apeb.vidhdr) ∧ buf = apeb.data) ∧ m = apeb.fill) ∧ (boolvar ↔ apeb.bad) ↔ apeb = mkpeb(aehdr, avhdr, buf, m, boolvar); (elim) Used terms: apeb, aehdr, avhdr, buf, m0, boolvar