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Proof step 90 from proof delta-wear-leveling (previous step)

# wlar1 = # wlar, # apebs = # wlar, # apebs0 = # wlar, avhdr0.leb = VTBL_LNUM, avhdr0.vol = VTBL_VOLID, apebs[n2] = mkpeb(aehdr, avhdr0, buf, m2, false), wlar[vtblpnum1] = wl-entry(m1, free), wlar[n2] = wl-entry(m0, used), apebs0[vtblpnum1] = mkpeb(aehdr0, avhdr, buf, align↑(datasize(buf, LEB_SIZE), EB_PAGE_SIZE), boolvar), wlar1[n2] = wl-entry(m0, stat), wlar1[vtblpnum1] = wl-entry(m1, stat0), ecs(wlar1) = ecs(wlar), Δ wlar1 = Δ wlar, vtblpnum1 < # wlar, n2 < # 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, avhdr0, buf, m2, false)), ubi-io-peb-inv(mkpeb(aehdr0, avhdr, buf, align↑(datasize(buf, LEB_SIZE), EB_PAGE_SIZE), boolvar)), unique-sqns(apebs), unique-sqns(apebs0), valid-ebatbl(apebs0, wlar1, vols, n0), valid-ebatbl(apebs, wlar, vols, n2), valid-eraseq(apebs, q), valid-eraseq(wlar, q), valid-eraseq(q), valid-eraseq(apebs0, q + eq-entry(n2, VTBL_VOLID × VTBL_LNUM) '), valid-eraseq(wlar1, q + eq-entry(n2, VTBL_VOLID × VTBL_LNUM) '), valid-eraseq(q + eq-entry(n2, VTBL_VOLID × VTBL_LNUM) '), valid-global-sqn(apebs, n1), valid-global-sqn(apebs0, n), valid-vtbl(apebs0, vols, wlar1, n0), valid-vtbl(apebs, vols, wlar, n2), valid-wl(apebs, wlar), valid-wl(apebs0, wlar1), m0 + WL_THRESHOLD ≤ m1, ecs(wlar).max ≤ m0 + UBI_ERASE_RETRIES, ∀ 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 obtained the following new goals

Proof step 91:
# 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

Rule argument

fma: m1 ∈ ecs(wlar)

Additional information

Used simplifier rules: ⊦ EB_PAGE_SIZE ≠ 0; (s)% ⊦ n < # wlar ∧ wlar[n] = wl-entry(m, stat) → m ∈ ecs(wlar); (ss)%n ≠ 0, m % n = 0 ⊦ align↑(m, n) = m; (s) Used formulas: m1 ∈ ecs(wlar)