| # wlar1 = # wlar, # apebs = # wlar, # apebs0 = # wlar, apebs[vtblpnum2] = mkpeb(aechdr(m0), avidhdr(v0, m3, valid-sqns(v, m, apebs).max, m5, m6), buf1, m2, false), wlar[vtblpnum1] = wl-entry(m4, free), wlar[vtblpnum2] = wl-entry(m0, used), vols[v][m] = ⌜vtblpnum2⌝ , ecs(wlar1) = ecs(wlar), err = ESUCCESS, 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(aechdr(m0), avidhdr(v0, m3, valid-sqns(v, m, apebs).max, m5, m6), buf1, m2, false)), unique-sqns(apebs), unique-sqns(apebs0), valid-ebatbl(apebs0, wlar1, vols0, n0), valid-eraseq(apebs, q), valid-eraseq(wlar, q), valid-eraseq(q), valid-eraseq(apebs0, q0), valid-eraseq(wlar1, q0), valid-eraseq(q0), valid-global-sqn(apebs, n1), valid-global-sqn(apebs0, n), valid-peb(v, m, mkpeb(aechdr(m0), avidhdr(v0, m3, valid-sqns(v, m, apebs).max, m5, m6), buf1, m2, false)), valid-vtbl(apebs0, vols0, wlar1, n0), valid-vtbl(apebs, vols, wlar, n2), valid-wl(apebs0, wlar1), v ∈ vols, m0 + WL_THRESHOLD ≤ m4, err = ESUCCESS → vols0 = vols[v, vols[v][m, ⌜vtblpnum1⌝ ]], err ≠ ESUCCESS → vols0 = vols, err = ESUCCESS → wlar1[vtblpnum1].ec = m4 ∧ wlar1[vtblpnum2].ec = m0, err ≠ ESUCCESS → q0.lebrefs = q.lebrefs, err = ESUCCESS → apebs0[vtblpnum1].fill = align↑(datasize(apebs0[vtblpnum1].data, LEB_SIZE), EB_PAGE_SIZE) ∧ apebs0[vtblpnum1].data = buf1 ∧ q0.lebrefs ⊆ q.lebrefs ++ (v × m), err = ESUCCESS → q0 = q + eq-entry(vtblpnum2, v × m) ', err = ESUCCESS ∨ ⌊err⌋ ⊦ [ubi_erase_worker_helper#(vtblpnum2; wlar1, apebs0; err); if err = ESUCCESS then q0 := q0.butlast] ( # apebs0 = # wlar1 ∧ unique-sqns(apebs0) ∧ valid-global-sqn(apebs0, n) ∧ valid-wl(apebs0, wlar1) ∧ valid-eraseq(q0) ∧ valid-eraseq(wlar1, q0) ∧ valid-eraseq(apebs0, q0) ∧ bflipset-cons(bflipset, wlar1) ∧ valid-ebatbl(apebs0, wlar1, vols0, n0) ∧ valid-vtbl(apebs0, vols0, wlar1, n0) ∧ ubi-io-inv(apebs0) ∧ ( vols = vols0 ∧ id(apebs0, apebs, mapped-pebs(vols0)) ∧ q0.lebrefs ⊆ q.lebrefs ++ (VTBL_VOLID × VTBL_LNUM) ∨ (∃ v, m, n. v ∈ vols ∧ m < # vols[v] ∧ vols[v][m] ≠ unmapped ∧ vols0 = vols[v, vols[v][m, ⌜n⌝ ]] ∧ id(apebs0, apebs, mapped-pebs(vols) -- vols[v][m].pnum) ∧ apebs0[n].data = apebs[vols[v][m].pnum].data ∧ apebs0[n].fill ≤ apebs[vols[v][m].pnum].fill ∧ q0.lebrefs ⊆ q.lebrefs ++ (v × m))) → err = ESUCCESS → Δ wlar1 < Δ wlar), vtblpnum1 = vtblpnum2, vtblpnum2 = n2, VTBL_VOLID ∈ vols, VTBL_VOLID ∈ vols0 |
# wlar1 = # wlar, # apebs = # wlar, # apebs0 = # wlar, apebs0[vtblpnum1].fill = align↑(datasize(apebs0[vtblpnum1].data, LEB_SIZE), EB_PAGE_SIZE), apebs[vtblpnum2] = mkpeb(aechdr(wlar1[vtblpnum2].ec), avidhdr(v0, m3, valid-sqns(v, m, apebs).max, m5, m6), apebs0[vtblpnum1].data, m2, false), wlar[vtblpnum1] = wl-entry(wlar1[vtblpnum1].ec, free), wlar[vtblpnum2] = wl-entry(wlar1[vtblpnum2].ec, used), vols[v][m] = ⌜vtblpnum2⌝ , ecs(wlar1) = ecs(wlar), Δ wlar1 = Δ wlar, vtblpnum1 ≠ vtblpnum2, vtblpnum2 ≠ n2, 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(aechdr(wlar1[vtblpnum2].ec), avidhdr(v0, m3, valid-sqns(v, m, apebs).max, m5, m6), apebs0[vtblpnum1].data, 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(wlar1[vtblpnum2].ec), avidhdr(v0, m3, valid-sqns(v, m, apebs).max, m5, m6), apebs0[vtblpnum1].data, m2, false)), valid-vtbl(apebs, vols, wlar, n2), valid-vtbl(apebs0, vols, wlar1, n0), valid-wl(apebs0, wlar1), v ∈ vols, wlar1[vtblpnum2].ec + WL_THRESHOLD ≤ wlar1[vtblpnum1].ec, ¬ VTBL_VOLID ∈ vols ⊦ [ubi_erase_worker_helper#(vtblpnum2; wlar1, apebs0; err); q0 := q + eq-entry(vtblpnum2, v × m) '; if err = ESUCCESS then q0 := q0.butlast] ( # apebs0 = # wlar1 ∧ unique-sqns(apebs0) ∧ valid-global-sqn(apebs0, n) ∧ valid-wl(apebs0, wlar1) ∧ valid-eraseq(q0) ∧ valid-eraseq(wlar1, q0) ∧ valid-eraseq(apebs0, q0) ∧ bflipset-cons(bflipset, wlar1) ∧ valid-ebatbl(apebs0, wlar1, vols[v, vols[v][m, ⌜vtblpnum1⌝ ]], n0) ∧ valid-vtbl(apebs0, vols, wlar1, n0) ∧ ubi-io-inv(apebs0) ∧ ( vols = vols[v, vols[v][m, ⌜vtblpnum1⌝ ]] ∧ id(apebs0, apebs, mapped-pebs(vols[v, vols[v][m, ⌜vtblpnum1⌝ ]])) ∧ q0.lebrefs ⊆ q.lebrefs ++ (VTBL_VOLID × VTBL_LNUM) ∨ (∃ v0, m0, n. v0 ∈ vols ∧ m0 < # vols[v0] ∧ vols[v0][m0] ≠ unmapped ∧ vols[v, vols[v][m, ⌜vtblpnum1⌝ ]] = vols[v0, vols[v0][m0, ⌜n⌝ ]] ∧ id(apebs0, apebs, mapped-pebs(vols) -- vols[v0][m0].pnum) ∧ apebs0[n].data = apebs[vols[v0][m0].pnum].data ∧ apebs0[n].fill ≤ apebs[vols[v0][m0].pnum].fill ∧ q0.lebrefs ⊆ q.lebrefs ++ (v0 × m0))) → err = ESUCCESS → Δ wlar1 < Δ wlar)
Used simplifier rules: ubi-io-inv-fwd: n < # apebs ⊦ apebs[n] = apeb ∧ ubi-io-inv(apebs) → ubi-io-peb-inv(apeb); (forward) from specification ubi-asm% ⊦ m < n → (n ≤ m ↔ false); (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ v ∈ vols[v0, ebatbl] ↔ v = v0 ∨ v ∈ vols; (ws)%⊦ v ∈ vols → ( valid-vtbl(apebs, vols[v, vols[v][m, ebae]], wlar, n0) ↔ valid-vtbl(apebs, vols, wlar, n0)); (s)% ⊦ lref ∈ s0 ++ lref0 ↔ lref = lref0 ∨ lref ∈ s0; (s)% ⊦ s0 ⊆ s0 ++ lref; (s)% ⊦ s1 ++ lref ⊆ s2 ↔ s1 ⊆ s2 ∧ lref ∈ s2; (ws)% ⊦ (q + eq-entry(n, v × m) ').lebrefs = q.lebrefs ++ (v × m); (s)% ⊦ eqent ∈ eqent0 ' ↔ eqent = eqent0; (s)% ⊦ eqent ∈ q + q0 ↔ eqent ∈ q ∨ eqent ∈ q0; (s)%a: ⊦ (q + q0) + q1 = q + q0 + q1; from specification list[erasequeue-base]%in-15: ⊦ q + eqent ' = q0 → eqent ∈ q0; (forward) from specification list[erasequeue-base]