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Proof step 6 from proof valid-wl-map (previous step)

# apebs = # wlar, apebs[n0].vidhdr.leb = VTBL_LNUM, apebs[m].vidhdr.leb = avhdr.leb, wlar[n0].status = used, wlar[m].status = used, apebs[n0].vidhdr.vol = VTBL_VOLID, apebs[m].vidhdr.vol = avhdr.vol, vols[avhdr.vol][avhdr.leb] = unmapped, apeb = mkpeb(aehdr, avhdr, buf, m1, boolvar), avhdr.leb < # vols[avhdr.vol], n < # wlar, n0 < # wlar, n1 < # wlar, m < # wlar, is-encoded(to-vtbl(vols), apebs[n0].data), valid-peb(apeb), 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, (wlar[n, wl-entry(aehdr.ec, used)][n1].status = erroneous ↔ apebs[n, apeb][n1].bad) ∧ (wlar[n, wl-entry(aehdr.ec, used)][n1].status = free → apebs[n1].vidhdr = empty) ∧ ( wlar[n, wl-entry(aehdr.ec, used)][n1].status ≠ erroneous ∧ wlar[n, wl-entry(aehdr.ec, used)][n1].status ≠ erasing → apebs[n, apeb][n1].echdr = aechdr(wlar[n, wl-entry(aehdr.ec, used)][n1].ec)) ∧ ( wlar[n, wl-entry(aehdr.ec, used)][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 simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
# apebs = # wlar, apebs[n0].vidhdr.leb = VTBL_LNUM, apebs[m].vidhdr.leb = avhdr.leb, wlar[n0].status = used, wlar[m].status = used, apebs[n0].vidhdr.vol = VTBL_VOLID, apebs[m].vidhdr.vol = avhdr.vol, vols[avhdr.vol][avhdr.leb] = unmapped, avhdr.leb < # vols[avhdr.vol], n < # wlar, n0 < # wlar, n1 < # wlar, m < # wlar, is-encoded(to-vtbl(vols), apebs[n0].data), 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, (wlar[n, wl-entry(aehdr.ec, used)][n1].status = erroneous ↔ apebs[n, mkpeb(aehdr, avhdr, buf, m1, boolvar)][n1].bad) ∧ (wlar[n, wl-entry(aehdr.ec, used)][n1].status = free → apebs[n1].vidhdr = empty) ∧ ( wlar[n, wl-entry(aehdr.ec, used)][n1].status ≠ erroneous ∧ wlar[n, wl-entry(aehdr.ec, used)][n1].status ≠ erasing → apebs[n, mkpeb(aehdr, avhdr, buf, m1, boolvar)][n1].echdr = aechdr(wlar[n, wl-entry(aehdr.ec, used)][n1].ec)) ∧ ( wlar[n, wl-entry(aehdr.ec, used)][n1].status = used → (∃ v, m. valid-peb(v, m, apebs[n, mkpeb(aehdr, avhdr, buf, m1, boolvar)][n1]) ∧ apebs[n, mkpeb(aehdr, avhdr, buf, m1, boolvar)][n1].vidhdr.sqn = valid-sqns(v, m, apebs[n, mkpeb(aehdr, avhdr, buf, m1, boolvar)]).max))

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic