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Proof step 164 from proof delta-wear-leveling (previous step)

# wlar1 = # wlar, # apebs = # wlar, # apebs0 = # wlar, wlar1[vtblpnum1] = wl-entry(m4, stat0), wlar1[vtblpnum2] = wl-entry(m1, stat), apebs0[vtblpnum1] = mkpeb(aehdr, avhdr, buf, align↑(datasize(buf, LEB_SIZE), EB_PAGE_SIZE), boolvar), apebs[vtblpnum2] = mkpeb(aechdr(m1), avidhdr(v0, m3, valid-sqns(v, m, apebs).max, m5, m6), buf, m2, false), wlar[vtblpnum1] = wl-entry(m4, free), wlar[vtblpnum2] = wl-entry(m1, used), vols[v][m] = ⌜vtblpnum2⌝ , ecs(wlar1) = ecs(wlar), Δ wlar1 = Δ wlar, m < # vols[v], vtblpnum1 < # wlar, vtblpnum2 < # wlar, bflipset-cons(bflipset0, wlar), bflipset-cons(bflipset, wlar1), id(apebs0, apebs, mapped-pebs(vols)), id○(apebs0, apebs, vtblpnum1), is-aligned(LEB_SIZE, EB_PAGE_SIZE), ubi-io-inv(apebs), ubi-io-inv(apebs0), ubi-io-peb-inv(mkpeb(aehdr, avhdr, buf, align↑(datasize(buf, LEB_SIZE), EB_PAGE_SIZE), boolvar)), ubi-io-peb-inv(mkpeb(aechdr(m1), avidhdr(v0, m3, valid-sqns(v, m, apebs).max, m5, m6), buf, m2, false)), unique-sqns(apebs), unique-sqns(apebs0), valid-ebatbl(apebs0, wlar1, vols[v, vols[v][m, ⌜vtblpnum1⌝ ]], n0), valid-eraseq(apebs, q), valid-eraseq(wlar, q), valid-eraseq(q), valid-eraseq(apebs0, q + eq-entry(vtblpnum2, v × m) '), valid-eraseq(wlar1, q + eq-entry(vtblpnum2, v × m) '), valid-eraseq(q + eq-entry(vtblpnum2, v × m) '), valid-global-sqn(apebs, n1), valid-global-sqn(apebs0, n), valid-peb(v, m, mkpeb(aechdr(m1), avidhdr(v0, m3, valid-sqns(v, m, apebs).max, m5, m6), buf, m2, false)), valid-vtbl(apebs, vols, wlar, n2), valid-vtbl(apebs0, vols, wlar1, n0), valid-wl(apebs0, wlar1), v ∈ vols, m4 ∈ ecs(wlar), ecs(wlar).max ≤ m1 + UBI_ERASE_RETRIES, m1 + WL_THRESHOLD ≤ m4 ⊦ vtblpnum1 = vtblpnum2, vtblpnum2 = n2, VTBL_VOLID ∈ vols

User applied rule cut formula

And closed the goal!

Rule argument

fma: m4 ≤ 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: m4 ≤ ecs(wlar).max