[Imprint][Data Privacy Statement][E-Mail]



View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 147 from proof delta-wear-leveling (previous step)

# apebs0 = # wlar, # apebs = # wlar, # wlar1 = # wlar, vols[v][m] = ⌜vtblpnum2⌝ , wlar[vtblpnum2] = wl-entry(m0, used), wlar[vtblpnum1] = wl-entry(m4, free), apebs[vtblpnum2] = mkpeb(aechdr(m0), avidhdr(v0, m3, valid-sqns(v, m, apebs).max, m5, m6), buf1, m2, false), ecs(wlar1) = ecs(wlar), Δ wlar1 = Δ wlar, vtblpnum1 ≠ vtblpnum2, vtblpnum2 ≠ n2, vtblpnum2 < # wlar, vtblpnum1 < # wlar, m < # vols[v], 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(aechdr(m0), avidhdr(v0, m3, valid-sqns(v, m, apebs).max, m5, m6), buf1, m2, false)), unique-sqns(apebs0), unique-sqns(apebs), valid-ebatbl(apebs0, wlar1, vols0, n0), valid-eraseq(q0), valid-eraseq(wlar1, q0), valid-eraseq(apebs0, q0), valid-eraseq(q), valid-eraseq(wlar, q), valid-eraseq(apebs, q), valid-global-sqn(apebs0, n), valid-global-sqn(apebs, n1), valid-peb(v, m, mkpeb(aechdr(m0), avidhdr(v0, m3, valid-sqns(v, m, apebs).max, m5, m6), buf1, m2, false)), valid-vtbl(apebs, vols, wlar, n2), valid-vtbl(apebs0, vols0, wlar1, n0), valid-wl(apebs0, wlar1), v ∈ vols, m0 + WL_THRESHOLD ≤ m4, ¬ VTBL_VOLID ∈ vols, ¬ VTBL_VOLID ∈ vols0, err = ESUCCESS → q0 = q + eq-entry(vtblpnum2, v × m) ', 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.lebrefs = q.lebrefs, err = ESUCCESS → wlar1[vtblpnum1].ec = m4 ∧ wlar1[vtblpnum2].ec = m0, err ≠ ESUCCESS → vols0 = vols, err = ESUCCESS → vols0 = vols[v, vols[v][m, ⌜vtblpnum1⌝ ]], err = ESUCCESS ∨ ⌊err⌋ ⊦ [if err ≠ ESUCCESS then debug#("ubi: wear-leveling of PEB " + vtblpnum2.toString + " to PEB " + vtblpnum1.toString + " failed"); if err = ESUCCESS then {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)

Heuristic conditional right split applied rule if right

And obtained the following new goals

Rule argument

pos: right 1

Additional information