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Proof step 91 from proof delta-wear-leveling (previous step)

# apebs0 = # wlar, # apebs = # wlar, # wlar1 = # wlar, avhdr0.leb = VTBL_LNUM, avhdr0.vol = VTBL_VOLID, wlar1[vtblpnum1] = wl-entry(m1, stat0), wlar1[n2] = wl-entry(m0, stat), apebs0[vtblpnum1] = mkpeb(aehdr0, avhdr, buf, align↑(datasize(buf, LEB_SIZE), EB_PAGE_SIZE), boolvar), wlar[n2] = wl-entry(m0, used), wlar[vtblpnum1] = wl-entry(m1, free), apebs[n2] = mkpeb(aehdr, avhdr0, buf, m2, false), ecs(wlar1) = ecs(wlar), Δ wlar1 = Δ wlar, n2 < # wlar, vtblpnum1 < # wlar, bflipset-cons(bflipset, wlar1), bflipset-cons(bflipset0, wlar), id(apebs0, apebs, mapped-pebs(vols)), id○(apebs0, apebs, vtblpnum1), is-aligned(LEB_SIZE, EB_PAGE_SIZE), ubi-io-inv(apebs0), ubi-io-inv(apebs), ubi-io-peb-inv(mkpeb(aehdr0, avhdr, buf, align↑(datasize(buf, LEB_SIZE), EB_PAGE_SIZE), boolvar)), ubi-io-peb-inv(mkpeb(aehdr, avhdr0, buf, m2, false)), unique-sqns(apebs0), unique-sqns(apebs), valid-ebatbl(apebs, wlar, vols, n2), valid-ebatbl(apebs0, wlar1, vols, n0), valid-eraseq(q + eq-entry(n2, VTBL_VOLID × VTBL_LNUM) '), valid-eraseq(wlar1, q + eq-entry(n2, VTBL_VOLID × VTBL_LNUM) '), valid-eraseq(apebs0, q + eq-entry(n2, VTBL_VOLID × VTBL_LNUM) '), valid-eraseq(q), valid-eraseq(wlar, q), valid-eraseq(apebs, q), valid-global-sqn(apebs0, n), valid-global-sqn(apebs, n1), valid-vtbl(apebs, vols, wlar, n2), valid-vtbl(apebs0, vols, wlar1, n0), valid-wl(apebs0, wlar1), valid-wl(apebs, wlar), m1 ∈ ecs(wlar), ecs(wlar).max ≤ m0 + UBI_ERASE_RETRIES, m0 + WL_THRESHOLD ≤ m1, ∀ v, m. ¬ v ∈ vols ∧ is-encoded(to-vtbl(vols)[v, m], buf) → valid-ebatbl(apebs0, wlar1, vols[v, fill(mkebatbl(m), unmapped)], n0) ∧ valid-vtbl(apebs0, vols[v, fill(mkebatbl(m), unmapped)], wlar1, n0) ⊦ vtblpnum1 = n2, VTBL_VOLID ∈ vols

User applied rule cut formula

And closed the goal!

Rule argument

fma: m1 ≤ ecs(wlar).max

Additional information

Used simplifier rules: ⊦ EB_PAGE_SIZE ≠ 0; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ n ∈ bag → ¬ bag.max < n; (s)%n ≠ 0, m % n = 0 ⊦ align↑(m, n) = m; (s)%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)% ⊦ ¬ WL_THRESHOLD ≤ UBI_ERASE_RETRIES; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m < n → (n ≤ m ↔ false); (s)%ubi-io-inv-fwd: n < # apebs ⊦ apebs[n] = apeb ∧ ubi-io-inv(apebs) → ubi-io-peb-inv(apeb); (forward) from specification ubi-asm Used formulas: m1 ≤ ecs(wlar).max