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Proof step 2 from proof valid-wl-use (previous step)

# apebs = # wlar, apeb.echdr.ec = m0, n < # apebs, valid-peb(apeb), valid-wl(apebs, wlar), 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 ⊦ valid-wl(apebs[n, apeb], wlar[n, wl-entry(m0, used)])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
# apebs = # wlar, n0 < # wlar, n < # wlar, valid-peb(apeb), 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)), ∀ m. m < # wlar ∧ m ≠ n ∧ wlar[m].status = used → apebs[m].vidhdr.vol ≠ apeb.vidhdr.vol ∨ apebs[m].vidhdr.leb ≠ apeb.vidhdr.leb ⊦ (wlar[n, wl-entry(apeb.echdr.ec, used)][n0].status = erroneous ↔ apebs[n, apeb][n0].bad) ∧ (wlar[n, wl-entry(apeb.echdr.ec, used)][n0].status = free → apebs[n0].vidhdr = empty) ∧ ( wlar[n, wl-entry(apeb.echdr.ec, used)][n0].status ≠ erroneous ∧ wlar[n, wl-entry(apeb.echdr.ec, used)][n0].status ≠ erasing → apebs[n, apeb][n0].echdr = aechdr(wlar[n, wl-entry(apeb.echdr.ec, used)][n0].ec)) ∧ ( wlar[n, wl-entry(apeb.echdr.ec, used)][n0].status = used → (∃ v, m. valid-peb(v, m, apebs[n, apeb][n0]) ∧ apebs[n, apeb][n0].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)));% ⊦ m < n → n ≠ 0; (s)%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)