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Proof step 4 from proof valid-wl-map (previous step)

# apebs = # wlar, apeb.echdr.ec = m0, vols[apeb.vidhdr.vol][apeb.vidhdr.leb] = unmapped, n < # apebs, apeb.vidhdr.leb < # vols[apeb.vidhdr.vol], valid-ebatbl(apebs, wlar, vols, n0), valid-peb(apeb), valid-vtbl(apebs, vols, wlar, n0), valid-wl(apebs, wlar), apeb.vidhdr.vol ∈ vols, valid-sqns(apeb.vidhdr.vol, apeb.vidhdr.leb, apebs) ≠ ∅ → apeb.vidhdr.sqn > valid-sqns(apeb.vidhdr.vol, apeb.vidhdr.leb, apebs).max ⊦ valid-wl(apebs[n, apeb], wlar[n, wl-entry(m0, used)]), VTBL_VOLID ∈ vols, n < # apebs ∧ # apebs = # wlar ∧ valid-wl(apebs, wlar) ∧ valid-peb(apeb) ∧ (valid-sqns(apeb.vidhdr.vol, apeb.vidhdr.leb, apebs) ≠ ∅ → apeb.vidhdr.sqn > valid-sqns(apeb.vidhdr.vol, apeb.vidhdr.leb, apebs).max) ∧ (∀ m. m < # wlar ∧ m ≠ n ∧ wlar[m].status = used → apebs[m].vidhdr.vol ≠ apeb.vidhdr.vol ∨ apebs[m].vidhdr.leb ≠ apeb.vidhdr.leb) ∧ apeb.echdr.ec = m0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
# apebs = # wlar, apebs[m].vidhdr.leb = apeb.vidhdr.leb, apebs[n0].vidhdr.leb = VTBL_LNUM, wlar[m].status = used, wlar[n0].status = used, apebs[m].vidhdr.vol = apeb.vidhdr.vol, apebs[n0].vidhdr.vol = VTBL_VOLID, vols[apeb.vidhdr.vol][apeb.vidhdr.leb] = unmapped, m < # wlar, n1 < # wlar, n0 < # wlar, n < # wlar, apeb.vidhdr.leb < # vols[apeb.vidhdr.vol], is-encoded(to-vtbl(vols), apebs[n0].data), valid-peb(apeb), apeb.vidhdr.vol ∈ vols, valid-sqns(apeb.vidhdr.vol, apeb.vidhdr.leb, apebs) ≠ ∅ → valid-sqns(apeb.vidhdr.vol, apeb.vidhdr.leb, apebs).max < apeb.vidhdr.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)), ∀ 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 ⊦ m = n, VTBL_VOLID ∈ vols, (wlar[n, wl-entry(apeb.echdr.ec, used)][n1].status = erroneous ↔ apebs[n, apeb][n1].bad) ∧ (wlar[n, wl-entry(apeb.echdr.ec, used)][n1].status = free → apebs[n1].vidhdr = empty) ∧ ( wlar[n, wl-entry(apeb.echdr.ec, used)][n1].status ≠ erroneous ∧ wlar[n, wl-entry(apeb.echdr.ec, used)][n1].status ≠ erasing → apebs[n, apeb][n1].echdr = aechdr(wlar[n, wl-entry(apeb.echdr.ec, used)][n1].ec)) ∧ ( wlar[n, wl-entry(apeb.echdr.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))

Rule argument

Additional information

Used simplifier rules: valid-wl: ⊦ valid-wl(apebs, wlar) ↔ (∀ 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)));%valid-vtbl: ⊦ valid-vtbl(apebs, vols, wlar, n0) ↔ n0 < # apebs ∧ n0 < # wlar ∧ wlar[n0].status = used ∧ apebs[n0].vidhdr.vol = VTBL_VOLID ∧ apebs[n0].vidhdr.leb = VTBL_LNUM ∧ is-encoded(to-vtbl(vols), apebs[n0].data);%valid-ebatbl: ⊦ valid-ebatbl(apebs, wlar, vols, n0) ↔ (∀ v, m, n. vols[v][m] = ⌜n⌝ ∧ v ∈ vols ∧ m < # vols[v] ↔ wlar[n].status = used ∧ n < # apebs ∧ n < # wlar ∧ apebs[n].vidhdr.valid? ∧ apebs[n].vidhdr.vol = v ∧ apebs[n].vidhdr.leb = m ∧ n ≠ n0);% ⊦ m < n → n ≠ 0; (s)%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m > n ↔ n < m; (s)%m ≠ n ⊦ apebs[m, apeb][n] = apebs[n]; (s)% ⊦ used ≠ free; (s)% ⊦ wl-entry(m, stat).status = stat; (s)% ⊦ m < # wlar → wlar[m, wle][m] = wle; (s)% ⊦ # wlar[n, wle] = # wlar; (s)