[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 61 from proof delta-wear-leveling (previous step)

# apebs = # wlar, avhdr0.leb = VTBL_LNUM, avhdr0.vol = VTBL_VOLID, wlar[n2] = wl-entry(m1, used), wlar[vtblpnum1] = wl-entry(m0, free), apebs[n2] = mkpeb(aehdr, avhdr0, buf1, m2, false), apebs1 = apebs, q1 = q, vols1 = vols, vtblpnum2 = n2, wlar0 = wlar, vtblpnum1 < # wlar, n2 < # wlar, bflipset-cons(bflipset0, wlar), ubi-io-inv(apebs), ubi-io-peb-inv(mkpeb(aehdr, 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-vtbl(apebs, vols, wlar, n2), valid-wl(apebs, wlar), m1 + WL_THRESHOLD ≤ m0, ¬ VTBL_VOLID ∈ vols ⊦ [ubi_atomic_leb_change# (avhdr0.vol, avhdr0.leb, vtblpnum1, LEB_SIZE, copy(apebs[n2].data, 0, mkbuf(LEB_SIZE), 0, LEB_SIZE), EB_PAGE_SIZE ; vols, wlar, q, bflipset0, n2, n1, apebs ; err0); 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) ∧ ¬ VTBL_VOLID ∈ vols ∧ 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 program lemma

And obtained the following new goals

Proof step 62:
wlar0 = wlar, n < # wlar, n1 < # wlar, n ≠ n1, v ∈ vols ∧ m < # vols[v] ∧ vols[v][m] = ⌜n1⌝ ∨ v = VTBL_VOLID ∧ m = VTBL_LNUM ∧ vtblpnum = n1 ⊦ [ubi_atomic_leb_change#(v, m, n, n0, buf, EB_PAGE_SIZE; vols, wlar, q, bflipset, vtblpnum, sqnum, apebs; err)] (Δ wlar = Δ wlar0 ∧ ecs(wlar) = ecs(wlar0) ∧ (err = ESUCCESS → wlar[n].ec = wlar0[n].ec ∧ wlar[n1].ec = wlar0[n1].ec))
Proof step 63:
# apebs = # wlar, avhdr0.leb = VTBL_LNUM, avhdr0.vol = VTBL_VOLID, apebs[n2] = mkpeb(aehdr, avhdr0, buf1, m2, false), wlar[vtblpnum1] = wl-entry(m0, free), wlar[n2] = wl-entry(m1, used), apebs1 = apebs, buf0 = copy(apebs[n2].data, 0, mkbuf(LEB_SIZE), 0, LEB_SIZE), m3 = avhdr0.leb, n3 = vtblpnum1, n4 = n2, n5 = LEB_SIZE, q1 = q, v0 = avhdr0.vol, vols1 = vols, vtblpnum2 = n2, wlar = wlar, wlar0 = wlar, wlar1 = wlar, vtblpnum1 < # wlar, n2 < # wlar, bflipset-cons(bflipset0, wlar), ubi-io-inv(apebs), ubi-io-peb-inv(mkpeb(aehdr, avhdr0, buf1, m2, false)), unique-sqns(apebs), valid-ebatbl(apebs, wlar, vols, n2), valid-eraseq(apebs, q), valid-eraseq(wlar, q), valid-eraseq(q), valid-global-sqn(apebs, n1), valid-vtbl(apebs, vols, wlar, n2), valid-wl(apebs, wlar), m1 + WL_THRESHOLD ≤ m0, avhdr0.vol ∈ vols ∧ avhdr0.leb < # vols[avhdr0.vol] ∧ vols[avhdr0.vol][avhdr0.leb] = ⌜n2⌝ ∨ avhdr0.vol = VTBL_VOLID ∧ avhdr0.leb = VTBL_LNUM ∧ n2 = n2 ⊦ [ubi_atomic_leb_change# (avhdr0.vol, avhdr0.leb, vtblpnum1, LEB_SIZE, copy(apebs[n2].data, 0, mkbuf(LEB_SIZE), 0, LEB_SIZE), EB_PAGE_SIZE ; vols, wlar, q, bflipset0, n2, n1, apebs ; err0)] ( Δ wlar = Δ wlar1 ∧ ecs(wlar) = ecs(wlar1) ∧ (err0 = ESUCCESS → wlar[n3].ec = wlar1[n3].ec ∧ wlar[n4].ec = wlar1[n4].ec) → [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) ∧ ¬ VTBL_VOLID ∈ vols ∧ 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)), vtblpnum1 = n2, VTBL_VOLID ∈ vols

Rule argument

spec: ubi-quality-base name: delta-atomic-leb-change seq: wlar0 = wlar, n < # wlar, n1 < # wlar, n ≠ n1, v ∈ vols ∧ m < # vols[v] ∧ vols[v][m] = ⌜n1⌝ ∨ v = VTBL_VOLID ∧ m = VTBL_LNUM ∧ vtblpnum = n1 ⊦ [ubi_atomic_leb_change# (v, m, n, n0, buf, EB_PAGE_SIZE ; vols, wlar, q, bflipset, vtblpnum, sqnum, apebs ; err)] ( Δ wlar = Δ wlar0 ∧ ecs(wlar) = ecs(wlar0) ∧ ( err = ESUCCESS → wlar[n].ec = wlar0[n].ec ∧ wlar[n1].ec = wlar0[n1].ec)) subst: [buf, n0, n, m, v, apebs, sqnum, vtblpnum, bflipset, q, wlar, vols, err, n1, wlar0] → [copy(apebs[n2].data, 0, mkbuf(LEB_SIZE), 0, LEB_SIZE), LEB_SIZE, vtblpnum1, avhdr0.leb, avhdr0.vol, apebs, n1, n2, bflipset0, q, wlar, vols, err0, n2, wlar] flags: <all paths>

Additional information

Used simplifier rules: ⊦ valid-vtbl(apebs, vols, wlar, n0) → n0 < # wlar; (ss)%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%valid-vtbl-wlar-status: ⊦ wlar[n0] = wl-entry(m, stat) ∧ valid-vtbl(apebs, vols, wlar, n0) → stat = used; (forward) from specification ubi-base% ⊦ used ≠ free; (s)