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

# apebs1 = # wlar, # apebs = # wlar, # wlar0 = # wlar, avhdr.leb = VTBL_LNUM, avhdr.vol = VTBL_VOLID, apebs[vtblpnum2] = mkpeb(aehdr1, avhdr, buf, m3, false), apebs[vtblpnum1] = mkpeb(aehdr, empty, mkempbuf(LEB_SIZE), 0, false), wlar[vtblpnum2] = wl-entry(m1, used), wlar[vtblpnum1] = wl-entry(m0, free), apebs1[vtblpnum1] = mkpeb(aehdr0, avhdr0, buf, align↑(datasize(buf, LEB_SIZE), EB_PAGE_SIZE), boolvar), aehdr.valid?, vtblpnum2 < # wlar, vtblpnum1 < # wlar, bflipset-cons(bflipset1, wlar0), bflipset-cons(bflipset, wlar), bflipset-cons(bflipset0, wlar), id(apebs1, apebs, mapped-pebs(vols)), id○(apebs1, apebs, vtblpnum1), is-aligned(LEB_SIZE, EB_PAGE_SIZE), ubi-io-inv(apebs1), ubi-io-inv(apebs), ubi-io-peb-inv(mkpeb(aehdr1, avhdr, buf, m3, false)), ubi-io-peb-inv(mkpeb(aehdr0, avhdr0, buf, align↑(datasize(buf, LEB_SIZE), EB_PAGE_SIZE), boolvar)), unique-sqns(apebs1), unique-sqns(apebs), valid-ebatbl(apebs, wlar, vols, vtblpnum4), valid-eraseq(q1), valid-eraseq(wlar0, q1), valid-eraseq(apebs1, q1), valid-eraseq(q), valid-eraseq(wlar, q), valid-eraseq(apebs, q), valid-global-sqn(apebs1, sqnum0), valid-global-sqn(apebs, sqnum), valid-peb(mkpeb(aehdr1, avhdr, buf, m3, false)), valid-vtbl(apebs, vols, wlar, vtblpnum4), valid-wl(apebs1, wlar0), valid-wl(apebs, wlar), q1.lebrefs ⊆ q.lebrefs ++ (avhdr.vol × avhdr.leb), bflipset = ∅ → m1 + WL_THRESHOLD ≤ m0, avhdr.vol ∈ vols ∨ is-encoded(to-vtbl(vols), buf) → valid-ebatbl(apebs1, wlar0, vols1, vtblpnum) ∧ valid-vtbl(apebs1, vols1, wlar0, vtblpnum), avhdr.vol = VTBL_VOLID ∧ avhdr.leb = VTBL_LNUM → (∀ v, m. ¬ v ∈ vols ∧ is-encoded(to-vtbl(vols)[v, m], buf) → valid-ebatbl(apebs1, wlar0, vols1[v, fill(mkebatbl(m), unmapped)], vtblpnum) ∧ valid-vtbl(apebs1, vols1[v, fill(mkebatbl(m), unmapped)], wlar0, vtblpnum)), avhdr.vol ∈ vols ∧ vols[avhdr.vol][avhdr.leb] ≠ unmapped → q1 = q + eq-entry(vols[avhdr.vol][avhdr.leb].pnum, avhdr.vol × avhdr.leb) ', avhdr.vol = VTBL_VOLID ∧ avhdr.leb = VTBL_LNUM → q1 = q + eq-entry(vtblpnum4, avhdr.vol × avhdr.leb) ', avhdr.vol = VTBL_VOLID ∧ avhdr.leb = VTBL_LNUM → vols1 = vols, avhdr.vol ∈ vols → vols1 = vols[avhdr.vol, vols[avhdr.vol][avhdr.leb, ⌜vtblpnum1⌝ ]] ⊦ ⟪ubi_erase_worker_helper#(vtblpnum2; wlar0, apebs1; err); if err = ESUCCESS then q1 := q1.butlast⟫ ( # apebs1 = # wlar0 ∧ unique-sqns(apebs1) ∧ valid-global-sqn(apebs1, sqnum0) ∧ valid-wl(apebs1, wlar0) ∧ valid-eraseq(q1) ∧ valid-eraseq(wlar0, q1) ∧ valid-eraseq(apebs1, q1) ∧ bflipset-cons(bflipset1, wlar0) ∧ valid-ebatbl(apebs1, wlar0, vols1, vtblpnum) ∧ valid-vtbl(apebs1, vols1, wlar0, vtblpnum) ∧ ubi-io-inv(apebs1) ∧ ( vols = vols1 ∧ id(apebs1, apebs, mapped-pebs(vols1)) ∧ q1.lebrefs ⊆ q.lebrefs ++ (VTBL_VOLID × VTBL_LNUM) ∨ (∃ v, m, n. v ∈ vols ∧ m < # vols[v] ∧ vols[v][m] ≠ unmapped ∧ vols1 = vols[v, vols[v][m, ⌜n⌝ ]] ∧ id(apebs1, apebs, mapped-pebs(vols) -- vols[v][m].pnum) ∧ apebs1[n].data = apebs[vols[v][m].pnum].data ∧ apebs1[n].fill ≤ apebs[vols[v][m].pnum].fill ∧ q1.lebrefs ⊆ q.lebrefs ++ (v × m)))), vtblpnum4 = vtblpnum1, VTBL_VOLID ∈ vols1, VTBL_VOLID ∈ vols, vtblpnum4 ∈ q, vtblpnum2 ∈ q

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 143:
# wlar0 = # wlar, # apebs = # wlar, # apebs1 = # wlar, avhdr.leb = VTBL_LNUM, avhdr.vol = VTBL_VOLID, apebs1[vtblpnum1] = mkpeb(aehdr0, avhdr0, buf, align↑(datasize(buf, LEB_SIZE), EB_PAGE_SIZE), boolvar), wlar[vtblpnum1] = wl-entry(m0, free), wlar[vtblpnum4] = wl-entry(m1, used), apebs[vtblpnum1] = mkpeb(aehdr, empty, mkempbuf(LEB_SIZE), 0, false), apebs[vtblpnum4] = mkpeb(aehdr1, avhdr, buf, m3, false), vtblpnum ≠ vtblpnum4, vtblpnum4 ≠ vtblpnum1, aehdr.valid?, vtblpnum1 < # wlar, vtblpnum4 < # wlar, bflipset-cons(bflipset0, wlar), bflipset-cons(bflipset, wlar), bflipset-cons(bflipset1, wlar0), id(apebs1, apebs, mapped-pebs(vols)), id○(apebs1, apebs, vtblpnum1), is-aligned(LEB_SIZE, EB_PAGE_SIZE), ubi-io-inv(apebs), ubi-io-inv(apebs1), ubi-io-peb-inv(mkpeb(aehdr0, avhdr0, buf, align↑(datasize(buf, LEB_SIZE), EB_PAGE_SIZE), boolvar)), ubi-io-peb-inv(mkpeb(aehdr1, avhdr, buf, m3, false)), unique-sqns(apebs), unique-sqns(apebs1), valid-ebatbl(apebs1, wlar0, vols, vtblpnum), valid-ebatbl(apebs, wlar, vols, vtblpnum4), valid-eraseq(apebs, q), valid-eraseq(wlar, q), valid-eraseq(q), valid-eraseq(apebs1, q + eq-entry(vtblpnum4, VTBL_VOLID × VTBL_LNUM) '), valid-eraseq(wlar0, q + eq-entry(vtblpnum4, VTBL_VOLID × VTBL_LNUM) '), valid-eraseq(q + eq-entry(vtblpnum4, VTBL_VOLID × VTBL_LNUM) '), valid-global-sqn(apebs, sqnum), valid-global-sqn(apebs1, sqnum0), valid-peb(mkpeb(aehdr1, avhdr, buf, m3, false)), valid-vtbl(apebs1, vols, wlar0, vtblpnum), valid-vtbl(apebs, vols, wlar, vtblpnum4), valid-wl(apebs, wlar), valid-wl(apebs1, wlar0), ¬ vtblpnum4 ∈ q, ¬ VTBL_VOLID ∈ vols, ¬ vtblpnum ∈ q, bflipset = ∅ → m1 + WL_THRESHOLD ≤ m0, ∀ v, m. ¬ v ∈ vols ∧ is-encoded(to-vtbl(vols)[v, m], buf) → valid-ebatbl(apebs1, wlar0, vols[v, fill(mkebatbl(m), unmapped)], vtblpnum) ∧ valid-vtbl(apebs1, vols[v, fill(mkebatbl(m), unmapped)], wlar0, vtblpnum) ⊦ ⟪ubi_erase_worker_helper#(vtblpnum4; wlar0, apebs1; err); q1 := q + eq-entry(vtblpnum4, VTBL_VOLID × VTBL_LNUM) '; if err = ESUCCESS then q1 := q1.butlast⟫ ( # apebs1 = # wlar0 ∧ unique-sqns(apebs1) ∧ valid-global-sqn(apebs1, sqnum0) ∧ valid-wl(apebs1, wlar0) ∧ valid-eraseq(q1) ∧ valid-eraseq(wlar0, q1) ∧ valid-eraseq(apebs1, q1) ∧ bflipset-cons(bflipset1, wlar0) ∧ valid-ebatbl(apebs1, wlar0, vols, vtblpnum) ∧ valid-vtbl(apebs1, vols, wlar0, vtblpnum) ∧ ubi-io-inv(apebs1) ∧ ( id(apebs1, apebs, mapped-pebs(vols)) ∧ q1.lebrefs ⊆ q.lebrefs ++ (VTBL_VOLID × VTBL_LNUM) ∨ (∃ v, m, n. v ∈ vols ∧ m < # vols[v] ∧ vols[v][m] ≠ unmapped ∧ vols = vols[v, vols[v][m, ⌜n⌝ ]] ∧ id(apebs1, apebs, mapped-pebs(vols) -- vols[v][m].pnum) ∧ apebs1[n].data = apebs[vols[v][m].pnum].data ∧ apebs1[n].fill ≤ apebs[vols[v][m].pnum].fill ∧ q1.lebrefs ⊆ q.lebrefs ++ (v × m))))

Rule argument

Additional information

Used simplifier rules: lf-vtbl-info: ⊦ valid-vtbl(apebs, vols, wlar, n) ∧ valid-eraseq(wlar, q) → ¬ n ∈ q;% ⊦ n ∈ q + eq-entry(n0, lref) ' ↔ n ∈ q ∨ n = n0; (ss)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (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%⊦ apebs[n0] = mkpeb(aehdr, avhdr, buf, m, boolvar) ∧ valid-vtbl(apebs, vols, wlar, n0) → is-encoded(to-vtbl(vols), buf); (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)%is-vtbl-pnum: n < # apebs, n < # wlar ⊦ apebs[n] = mkpeb(aehdr, avhdr, buf, m, boolvar) ∧ wlar[n] = wl-entry(m0, used) ∧ valid-wl(apebs, wlar) ∧ avhdr.vol = VTBL_VOLID ∧ avhdr.leb = VTBL_LNUM ∧ valid-ebatbl(apebs, wlar, vols, n0) ∧ ¬ VTBL_VOLID ∈ vols → n = n0; (forward) from specification ubi-base%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]