[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 18 from proof inv-wl-worker (previous step)

# apebs = # wlar, wlar[vtblpnum].status = used, wlar[vtblpnum0] = wl-entry(m0, stat), stat = free, vtblpnum0 < # wlar, vtblpnum < # wlar, bflipset-cons(bflipset0, wlar), bflipset-cons(bflipset, wlar), ubi-io-inv(apebs), unique-sqns(apebs), valid-ebatbl(apebs, wlar, vols, vtblpnum4), valid-eraseq(apebs, q), valid-eraseq(wlar, q), valid-eraseq(q), valid-global-sqn(apebs, sqnum), valid-vtbl(apebs, vols, wlar, vtblpnum4), valid-wl(apebs, wlar), bflipset = ∅ → wlar[vtblpnum].ec + WL_THRESHOLD ≤ m0 ⊦ ⟪aubi_io_read_vidhdr#(vtblpnum, apebs; avhdr; bitflips, err); vols0 := vols; q0 := q; apebs0 := apebs; if err = ESUCCESS then let buf = mkbuf(LEB_SIZE) in {aubi_io_read_data#(vtblpnum, 0, 0, LEB_SIZE, apebs; buf; bitflips, err); if err = ESUCCESS then ubi_atomic_leb_change# (avhdr.vol, avhdr.leb, vtblpnum0, LEB_SIZE, buf, EB_PAGE_SIZE; vols, wlar, q, bflipset0, vtblpnum4, sqnum, apebs; err); if err ≠ ESUCCESS then debug#("ubi: wear-leveling of PEB " + vtblpnum.toString + " to PEB " + vtblpnum0.toString + " failed"); if err = ESUCCESS then {ubi_erase_worker_helper#(vtblpnum; wlar, apebs; err); if err = ESUCCESS then q := q.butlast}}⟫ ( # apebs = # wlar ∧ unique-sqns(apebs) ∧ valid-global-sqn(apebs, sqnum) ∧ 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, vtblpnum4) ∧ valid-vtbl(apebs, vols, wlar, vtblpnum4) ∧ ubi-io-inv(apebs) ∧ ( vols0 = vols ∧ id(apebs, apebs0, mapped-pebs(vols)) ∧ q.lebrefs ⊆ q0.lebrefs ++ (VTBL_VOLID × VTBL_LNUM) ∨ (∃ v, m, n. v ∈ vols0 ∧ m < # vols0[v] ∧ vols0[v][m] ≠ unmapped ∧ vols = vols0[v, vols0[v][m, ⌜n⌝ ]] ∧ id(apebs, apebs0, mapped-pebs(vols0) -- vols0[v][m].pnum) ∧ apebs[n].data = apebs0[vols0[v][m].pnum].data ∧ apebs[n].fill ≤ apebs0[vols0[v][m].pnum].fill ∧ q.lebrefs ⊆ q0.lebrefs ++ (v × m)))), VTBL_VOLID ∈ vols, vtblpnum4 ∈ q

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 19:
# apebs = # wlar, apebs[vtblpnum0].fill = 0, wlar[vtblpnum].status = used, apebs[vtblpnum0].vidhdr = empty, wlar[vtblpnum0] = wl-entry(m0, free), vtblpnum4 ≠ vtblpnum0, apebs[vtblpnum0].echdr.valid?, vtblpnum < # wlar, vtblpnum0 < # wlar, bflipset-cons(bflipset, wlar), bflipset-cons(bflipset0, wlar), ubi-io-inv(apebs), unique-sqns(apebs), valid-ebatbl(apebs, wlar, vols, vtblpnum4), valid-eraseq(q), valid-eraseq(wlar, q), valid-eraseq(apebs, q), valid-global-sqn(apebs, sqnum), valid-vtbl(apebs, vols, wlar, vtblpnum4), valid-wl(apebs, wlar), ¬ vtblpnum4 ∈ q, ¬ VTBL_VOLID ∈ vols, bflipset = ∅ → wlar[vtblpnum].ec + WL_THRESHOLD ≤ m0 ⊦ ⟪aubi_io_read_vidhdr#(vtblpnum, apebs; avhdr; bitflips, err); vols0 := vols; q0 := q; apebs0 := apebs; if err = ESUCCESS then let buf = mkbuf(LEB_SIZE) in {aubi_io_read_data#(vtblpnum, 0, 0, LEB_SIZE, apebs; buf; bitflips, err); if err = ESUCCESS then ubi_atomic_leb_change# (avhdr.vol, avhdr.leb, vtblpnum0, LEB_SIZE, buf, EB_PAGE_SIZE; vols, wlar, q, bflipset0, vtblpnum4, sqnum, apebs; err); if err ≠ ESUCCESS then debug#("ubi: wear-leveling of PEB " + vtblpnum.toString + " to PEB " + vtblpnum0.toString + " failed"); if err = ESUCCESS then {ubi_erase_worker_helper#(vtblpnum; wlar, apebs; err); if err = ESUCCESS then q := q.butlast}}⟫ ( # apebs = # wlar ∧ unique-sqns(apebs) ∧ valid-global-sqn(apebs, sqnum) ∧ 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, vtblpnum4) ∧ valid-vtbl(apebs, vols, wlar, vtblpnum4) ∧ ubi-io-inv(apebs) ∧ ( vols0 = vols ∧ id(apebs, apebs0, mapped-pebs(vols)) ∧ q.lebrefs ⊆ q0.lebrefs ++ (VTBL_VOLID × VTBL_LNUM) ∨ (∃ v, m, n. v ∈ vols0 ∧ m < # vols0[v] ∧ vols0[v][m] ≠ unmapped ∧ vols = vols0[v, vols0[v][m, ⌜n⌝ ]] ∧ id(apebs, apebs0, mapped-pebs(vols0) -- vols0[v][m].pnum) ∧ apebs[n].data = apebs0[vols0[v][m].pnum].data ∧ apebs[n].fill ≤ apebs0[vols0[v][m].pnum].fill ∧ q.lebrefs ⊆ q0.lebrefs ++ (v × m))))

Rule argument

Additional information

Used simplifier rules: lf-valid-vtbl-neq-free: ⊦ wlar[m] = wl-entry(m0, free) ∧ valid-vtbl(apebs, vols, wlar, n) → n ≠ m;%lf-valid-wl-free-emptyvidhdr: n < # wlar, n < # apebs ⊦ wlar[n] = wl-entry(m, free) ∧ valid-wl(apebs, wlar) ∧ ubi-io-inv(apebs) → apebs[n].vidhdr = empty ∧ apebs[n].echdr.valid? ∧ apebs[n].fill = 0;