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Proof step 126 from proof delta-wear-leveling (previous step)

# apebs = # wlar, avhdr0.sqn = valid-sqns(v, m, apebs).max, wlar[vtblpnum2] = wl-entry(m1, used), wlar[vtblpnum1] = wl-entry(m0, free), apebs[vtblpnum2] = mkpeb(aechdr(m1), avhdr0, buf1, m2, false), apebs1 = apebs, q1 = q, vols1 = vols, vtblpnum3 = n2, wlar0 = wlar, m < # vols[v], vtblpnum2 < # wlar, vtblpnum1 < # wlar, bflipset-cons(bflipset0, wlar), is-aligned(LEB_SIZE, EB_PAGE_SIZE), ubi-io-inv(apebs), ubi-io-peb-inv(mkpeb(aechdr(m1), avhdr0, buf1, m2, false)), unique-sqns(apebs), valid-ebatbl(apebs, wlar, vols, n2), valid-eraseq(q), valid-eraseq(wlar, q), valid-eraseq(apebs, q), valid-global-sqn(apebs, n1), valid-peb(v, m, mkpeb(aechdr(m1), avhdr0, buf1, m2, false)), valid-vtbl(apebs, vols, wlar, n2), v ∈ vols, m1 + WL_THRESHOLD ≤ m0, ¬ VTBL_VOLID ∈ vols ⊦ [ubi_atomic_leb_change# (avhdr0.vol, avhdr0.leb, vtblpnum1, LEB_SIZE, copy(apebs[vtblpnum2].data, 0, mkbuf(LEB_SIZE), 0, LEB_SIZE), EB_PAGE_SIZE ; vols, wlar, q, bflipset0, n2, n1, apebs ; err0)] ( (err0 = ESUCCESS ∨ ⌊err0⌋ ) ∧ id○(apebs, apebs1, vtblpnum1) ∧ ubi-io-inv(apebs) ∧ # apebs = # wlar ∧ unique-sqns(apebs) ∧ valid-global-sqn(apebs, n1) ∧ valid-wl(apebs, wlar) ∧ valid-eraseq(q) ∧ valid-eraseq(wlar, q) ∧ valid-eraseq(apebs, q) ∧ ¬ VTBL_VOLID ∈ vols ∧ bflipset-cons(bflipset0, wlar) ∧ (v ∈ vols1 ∨ is-encoded(to-vtbl(vols1), buf1) ∨ err0 ≠ ESUCCESS → valid-ebatbl(apebs, wlar, vols, n2) ∧ valid-vtbl(apebs, vols, wlar, n2)) ∧ ( err0 = ESUCCESS ∧ v = VTBL_VOLID ∧ m = VTBL_LNUM → (∀ v, m. ¬ v ∈ vols1 ∧ is-encoded(to-vtbl(vols1)[v, m], buf1) → valid-ebatbl(apebs, wlar, vols[v, fill(mkebatbl(m), unmapped)], n2) ∧ valid-vtbl(apebs, vols[v, fill(mkebatbl(m), unmapped)], wlar, n2))) ∧ (err0 = ESUCCESS ∧ v ∈ vols1 ∧ vols1[v][m] ≠ unmapped → q = q1 + eq-entry(vols1[v][m].pnum, v × m) ') ∧ (err0 = ESUCCESS ∧ v = VTBL_VOLID ∧ m = VTBL_LNUM → q = q1 + eq-entry(vtblpnum3, VTBL_VOLID × VTBL_LNUM) ') ∧ id(apebs, apebs1, mapped-pebs(vols1)) ∧ (v = VTBL_VOLID ∧ m = VTBL_LNUM ∨ err0 ≠ ESUCCESS → vols = vols1) ∧ (v ∈ vols1 ∧ err0 = ESUCCESS → vols = vols1[v, vols1[v][m, ⌜vtblpnum1⌝ ]]) ∧ ( err0 = ESUCCESS → apebs[vtblpnum1].fill = align↑(datasize(apebs[vtblpnum1].data, LEB_SIZE), EB_PAGE_SIZE) ∧ apebs[vtblpnum1].data = buf1 ∧ q.lebrefs ⊆ q1.lebrefs ++ (v × m)) ∧ (err0 ≠ ESUCCESS → q.lebrefs = q1.lebrefs) → [if err0 ≠ ESUCCESS then debug#("ubi: wear-leveling of PEB " + vtblpnum2.toString + " to PEB " + vtblpnum1.toString + " failed"); if err0 = ESUCCESS then {ubi_erase_worker_helper#(vtblpnum2; wlar, apebs; err0); if err0 = ESUCCESS then q := q.butlast}] ( # apebs = # wlar ∧ unique-sqns(apebs) ∧ valid-global-sqn(apebs, n1) ∧ valid-wl(apebs, wlar) ∧ valid-eraseq(q) ∧ valid-eraseq(wlar, q) ∧ valid-eraseq(apebs, q) ∧ bflipset-cons(bflipset0, wlar) ∧ valid-ebatbl(apebs, wlar, vols, n2) ∧ valid-vtbl(apebs, vols, wlar, n2) ∧ ubi-io-inv(apebs) ∧ ( vols1 = vols ∧ id(apebs, apebs1, mapped-pebs(vols)) ∧ q.lebrefs ⊆ q1.lebrefs ++ (VTBL_VOLID × VTBL_LNUM) ∨ (∃ v, m, n. v ∈ vols1 ∧ m < # vols1[v] ∧ vols1[v][m] ≠ unmapped ∧ vols = vols1[v, vols1[v][m, ⌜n⌝ ]] ∧ id(apebs, apebs1, mapped-pebs(vols1) -- vols1[v][m].pnum) ∧ apebs[n].data = apebs1[vols1[v][m].pnum].data ∧ apebs[n].fill ≤ apebs1[vols1[v][m].pnum].fill ∧ q.lebrefs ⊆ q1.lebrefs ++ (v × m))) → err0 = ESUCCESS → Δ wlar < Δ wlar0))

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: ubi-base name: valid-ebatbl seq: ⊦ valid-ebatbl(apebs, wlar, vols, n0) ↔ (∀ v, m, n. vols[v][m] = ⌜n⌝ ∧ v ∈ vols ∧ m < # vols[v] ↔ wlar[n].status = used ∧ n < # apebs ∧ n < # wlar ∧ apebs[n].vidhdr.valid? ∧ apebs[n].vidhdr.vol = v ∧ apebs[n].vidhdr.leb = m ∧ n ≠ n0) subst: [n0, vols, wlar, apebs] → [n2, vols, wlar, apebs] flags: <all paths>

Additional information

Used terms: n2, vols, wlar, apebs