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Proof step 101 from proof delta-wear-leveling (previous step)

# wlar1 = # wlar, # apebs = # wlar, # apebs0 = # wlar, # apebs1 = # wlar0, Δ wlar0 + m = Δ wlar, avhdr0.leb = VTBL_LNUM, avhdr0.vol = VTBL_VOLID, apebs1[n3] = mkpeb(aehdr1, avhdr1, buf0, m4, boolvar0), 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), apebs[vols[v][m3].pnum] = mkpeb(aehdr2, avhdr2, buf1, m5, boolvar1), ecs(wlar1) = ecs(wlar), Δ wlar1 = Δ wlar, vtblpnum1 < # wlar, n2 < # wlar, m0 + UBI_ERASE_RETRIES < ecs(wlar).max, bflipset-cons(bflipset0, wlar), bflipset-cons(bflipset, wlar1), bflipset-cons(bflipset, wlar0), 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-inv(apebs1), 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), unique-sqns(apebs1), valid-ebatbl(apebs0, wlar1, vols, n0), valid-ebatbl(apebs, wlar, vols, n2), valid-ebatbl(apebs1, wlar0, vols, n0), valid-eraseq(apebs, q), valid-eraseq(wlar, 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-eraseq(apebs1, q), valid-eraseq(wlar0, q), valid-eraseq(q), valid-global-sqn(apebs, n1), valid-global-sqn(apebs0, n), valid-global-sqn(apebs1, n), valid-vtbl(apebs0, vols, wlar1, n0), valid-vtbl(apebs, vols, wlar, n2), valid-vtbl(apebs1, vols, wlar0, n0), valid-wl(apebs, wlar), valid-wl(apebs0, wlar1), valid-wl(apebs1, wlar0), m ≤ UBI_ERASE_RETRIES + 1, m0 + WL_THRESHOLD ≤ m1, Δ wlar ≤ Δ wlar0, ∀ 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), id(apebs1, apebs, mapped-pebs(vols)) ∨ v ∈ vols ∧ m3 < # vols[v] ∧ vols[v][m3] ≠ unmapped ∧ vols = vols[v, vols[v][m3, ⌜n3⌝ ]] ∧ id(apebs1, apebs, mapped-pebs(vols) -- vols[v][m3].pnum) ∧ buf0 = buf1 ∧ m4 ≤ m5 ⊦ m = 0, vtblpnum1 = n2, VTBL_VOLID ∈ vols

User applied rule insert equation

And closed the goal!

Rule argument

pos: left 5 flags: rotate, discard

Additional information

Used simplifier rules: ⊦ EB_PAGE_SIZE ≠ 0; (s)% ⊦ m + m0 ≤ m ↔ m0 = 0; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%n ≠ 0, m % n = 0 ⊦ align↑(m, n) = m; (s)