| # apebs = n1 + vtblpnum1, # wlar0 = n1 + vtblpnum1, apebs[vtblpnum1] = mkpeb(aechdr(m), avidhdr(v, m1, m2, m3, m4), buf1, m0, false), avhdr = apebs[vtblpnum1].vidhdr, ¬ bitflips, ¬ bitflips0, buf = mkbuf(LEB_SIZE), err = ESUCCESS, err = err0, ladr = apebs[vtblpnum1].vidhdr.vol × apebs[vtblpnum1].vidhdr.leb, n = 0, vtblpnum0 = recs[ladr].pnum, wlar = wlar1[vtblpnum1, wl-entry(wlar1[vtblpnum1].ec, used)], wlar1 = wlar0[vtblpnum1, wlar0[vtblpnum1].ec:= m], apebs[vtblpnum1].vidhdr.valid?, vtblpnum0 < # wlar, vtblpnum1 < # wlar1, vtblpnum1 < # wlar0, nx < vtblpnum1, vtblpnum1 < # apebs, bflipset-cons(bflipset, subarray(wlar0, 0, vtblpnum1)), indices-erasing(wlar0, nx), ubi-io-inv(apebs), ubi-io-peb-inv(mkpeb(aechdr(m), avidhdr(v, m1, m2, m3, m4), buf1, m0, false)), unique-sqns(apebs), valid-eraseq(subarray(wlar0, 0, vtblpnum1), q), valid-eraseq-stronger(subarray(apebs, 0, vtblpnum1), q), valid-global-sqn(subarray(apebs, 0, vtblpnum1), sqnum), valid-recs(subarray(apebs, 0, vtblpnum1), subarray(wlar0, 0, vtblpnum1), recs), valid-recs-sqns(apebs, recs), valid-wl(subarray(apebs, 0, vtblpnum1), subarray(wlar0, 0, vtblpnum1)), ladr ∈ recs, recs[ladr].sqn ≤ apebs[vtblpnum1].vidhdr.sqn, 0 + LEB_SIZE ≤ # buf, 0 + LEB_SIZE ≤ # apebs[vtblpnum1].data, apebs[vtblpnum1].vidhdr.size ≠ 0 → apebs[vtblpnum1].vidhdr.size ≤ datasize(copy(apebs[vtblpnum1].data, 0, buf, 0, LEB_SIZE)) ∧ apebs[vtblpnum1].vidhdr.checksum = checksum(copy(apebs[vtblpnum1].data, 0, buf, 0, LEB_SIZE), apebs[vtblpnum1].vidhdr.size), apebs[vtblpnum1].vidhdr.size ≠ 0 → ( (apebs[vtblpnum1].vidhdr.valid? ∧ vtblpnum1 < # apebs) ∧ (0 + LEB_SIZE ≤ # apebs[vtblpnum1].data ∧ 0 + LEB_SIZE ≤ # buf) ∧ vtblpnum1 < # apebs) ∧ ( apebs[vtblpnum1].vidhdr.size ≤ datasize(copy(apebs[vtblpnum1].data, 0, buf, 0, LEB_SIZE)) → (apebs[vtblpnum1].vidhdr.valid? ∧ vtblpnum1 < # apebs) ∧ ((0 + LEB_SIZE ≤ # apebs[vtblpnum1].data ∧ 0 + LEB_SIZE ≤ # buf) ∧ vtblpnum1 < # apebs) ∧ apebs[vtblpnum1].vidhdr.valid? ∧ vtblpnum1 < # apebs), ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ ⟪q := q + eq-entry(vtblpnum0, avhdr.vol × avhdr.leb) '; recs[ladr] := recovery-entry(vtblpnum1, avhdr.sqn); vtblpnum := vtblpnum1 + 1⟫ ( vtblpnum ≤ # apebs ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ ( err = ESUCCESS → # apebs = # wlar[vtblpnum0, wl-entry(wlar[vtblpnum0].ec, erasing)] ∧ nx < vtblpnum ∧ indices-erasing(wlar[vtblpnum0, wl-entry(wlar[vtblpnum0].ec, erasing)], nx) ∧ valid-global-sqn(subarray(apebs, 0, vtblpnum), max(sqnum, apebs[vtblpnum1].vidhdr.sqn + 1)) ∧ valid-eraseq(subarray(wlar[vtblpnum0, wl-entry(wlar[vtblpnum0].ec, erasing)], 0, vtblpnum), q) ∧ bflipset-cons(bflipset -- vtblpnum0, subarray(wlar[vtblpnum0, wl-entry(wlar[vtblpnum0].ec, erasing)], 0, vtblpnum)) ∧ valid-eraseq-stronger(subarray(apebs, 0, vtblpnum), q) ∧ valid-wl(subarray(apebs, 0, vtblpnum), subarray(wlar[vtblpnum0, wl-entry(wlar[vtblpnum0].ec, erasing)], 0, vtblpnum)) ∧ valid-recs-sqns(apebs, recs) ∧ valid-recs(subarray(apebs, 0, vtblpnum), subarray(wlar[vtblpnum0, wl-entry(wlar[vtblpnum0].ec, erasing)], 0, vtblpnum), recs)) ∧ # apebs < n1 + vtblpnum), m3 = 0, n1 = 0, dups(nx) |
# wlar0 = n1 + vtblpnum1, # apebs = n1 + vtblpnum1, apebs[vtblpnum1] = mkpeb(aechdr(m), avidhdr(v, m1, m2, m3, m4), buf1, m0, false), avhdr = apebs[vtblpnum1].vidhdr, ¬ bitflips, ¬ bitflips0, buf = mkbuf(LEB_SIZE), err = err0, err = ESUCCESS, ladr = apebs[vtblpnum1].vidhdr.vol × apebs[vtblpnum1].vidhdr.leb, n = 0, vtblpnum0 = recs[ladr].pnum, wlar = wlar1[vtblpnum1, wl-entry(wlar1[vtblpnum1].ec, used)], wlar1 = wlar0[vtblpnum1, wlar0[vtblpnum1].ec:= m], avhdr.valid?, apebs[vtblpnum1].vidhdr.valid?, vtblpnum1 < # apebs, nx < vtblpnum1, vtblpnum1 < # wlar0, vtblpnum1 < # wlar1, vtblpnum0 < # wlar, bflipset-cons(bflipset, subarray(wlar0, 0, vtblpnum1)), indices-erasing(wlar0, nx), ubi-io-inv(apebs), ubi-io-peb-inv(mkpeb(aechdr(m), avidhdr(v, m1, m2, m3, m4), buf1, m0, false)), unique-sqns(apebs), valid-eraseq(subarray(wlar0, 0, vtblpnum1), q), valid-eraseq-stronger(subarray(apebs, 0, vtblpnum1), q), valid-global-sqn(subarray(apebs, 0, vtblpnum1), sqnum), valid-recs(subarray(apebs, 0, vtblpnum1), subarray(wlar0, 0, vtblpnum1), recs), valid-recs-sqns(apebs, recs), valid-wl(subarray(apebs, 0, vtblpnum1), subarray(wlar0, 0, vtblpnum1)), ladr ∈ recs, 0 + LEB_SIZE ≤ # apebs[vtblpnum1].data, 0 + LEB_SIZE ≤ # buf, recs[ladr].sqn ≤ apebs[vtblpnum1].vidhdr.sqn, apebs[vtblpnum1].vidhdr.size ≠ 0 → ( (apebs[vtblpnum1].vidhdr.valid? ∧ vtblpnum1 < # apebs) ∧ (0 + LEB_SIZE ≤ # apebs[vtblpnum1].data ∧ 0 + LEB_SIZE ≤ # buf) ∧ vtblpnum1 < # apebs) ∧ ( apebs[vtblpnum1].vidhdr.size ≤ datasize(copy(apebs[vtblpnum1].data, 0, buf, 0, LEB_SIZE)) → (apebs[vtblpnum1].vidhdr.valid? ∧ vtblpnum1 < # apebs) ∧ ((0 + LEB_SIZE ≤ # apebs[vtblpnum1].data ∧ 0 + LEB_SIZE ≤ # buf) ∧ vtblpnum1 < # apebs) ∧ apebs[vtblpnum1].vidhdr.valid? ∧ vtblpnum1 < # apebs), apebs[vtblpnum1].vidhdr.size ≠ 0 → apebs[vtblpnum1].vidhdr.size ≤ datasize(copy(apebs[vtblpnum1].data, 0, buf, 0, LEB_SIZE)) ∧ apebs[vtblpnum1].vidhdr.checksum = checksum(copy(apebs[vtblpnum1].data, 0, buf, 0, LEB_SIZE), apebs[vtblpnum1].vidhdr.size), ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ ⟪recs[ladr] := recovery-entry(vtblpnum1, avhdr.sqn); vtblpnum := vtblpnum1 + 1⟫ ( vtblpnum ≤ # apebs ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ ( err = ESUCCESS → # apebs = # wlar[vtblpnum0, wl-entry(wlar[vtblpnum0].ec, erasing)] ∧ nx < vtblpnum ∧ indices-erasing(wlar[vtblpnum0, wl-entry(wlar[vtblpnum0].ec, erasing)], nx) ∧ valid-global-sqn(subarray(apebs, 0, vtblpnum), max(sqnum, apebs[vtblpnum1].vidhdr.sqn + 1)) ∧ valid-eraseq (subarray(wlar[vtblpnum0, wl-entry(wlar[vtblpnum0].ec, erasing)], 0, vtblpnum), q + eq-entry(vtblpnum0, avhdr.vol × avhdr.leb) ') ∧ bflipset-cons(bflipset -- vtblpnum0, subarray(wlar[vtblpnum0, wl-entry(wlar[vtblpnum0].ec, erasing)], 0, vtblpnum)) ∧ valid-eraseq-stronger(subarray(apebs, 0, vtblpnum), q + eq-entry(vtblpnum0, avhdr.vol × avhdr.leb) ') ∧ valid-wl(subarray(apebs, 0, vtblpnum), subarray(wlar[vtblpnum0, wl-entry(wlar[vtblpnum0].ec, erasing)], 0, vtblpnum)) ∧ valid-recs-sqns(apebs, recs) ∧ valid-recs(subarray(apebs, 0, vtblpnum), subarray(wlar[vtblpnum0, wl-entry(wlar[vtblpnum0].ec, erasing)], 0, vtblpnum), recs)) ∧ # apebs < n1 + vtblpnum), m3 = 0, n1 = 0, dups(nx)
Used simplifier rules: ⊦ n + 0 = n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ # mkbuf(n) = n; (s)% ⊦ m ≤ m; (s)% ⊦ m < # wlar → wlar[m, wle][m] = wle; (s)% ⊦ (wle.ec:= m).ec = m; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m + m0 ≤ m ↔ m0 = 0; (s)%m < # wlar ⊦ wlar[m, wle][m, wle0] = wlar[m, wle0]; (s)% ⊦ # wlar[n, wle] = # wlar; (s)% ⊦ ¬ ⌊ESUCCESS⌋ ; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).data = buf; (s)%⊦ ubi-io-peb-inv(mkpeb(aehdr, avhdr, buf, n, boolvar)) → # buf = LEB_SIZE; (s)%# buf = m, # buf0 = m ⊦ copy(buf, 0, buf0, 0, m) = buf; (s)