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Proof step 31 from proof inv-write (previous step)

# apebs0 = # wlar, # apebs1 = # wlar, wlar[m0] = wl-entry(m1, used), apebs1[m0] = mkpeb(aehdr, avhdr, buf2, m, false), vols[v][vtblpnum4] = ⌜m0⌝ , apebs = apebs0, buf0 = buf1, buf1 = mkbuf(vtblpnum3 + n2), n = vtblpnum3, n0 = 0, vtblpnum = 0, vtblpnum0 = m0, vtblpnum4 < # vols[v], m0 < # wlar, bflipset-cons(bflipset, wlar), is-aligned(vtblpnum3, EB_PAGE_SIZE), is-aligned(n2, EB_PAGE_SIZE), ubi-io-inv(apebs0), ubi-io-inv(apebs1), ubi-io-peb-inv(mkpeb(aehdr, avhdr, buf2, m, false)), ubi-io-read-data-pre(vtblpnum0, vtblpnum, n0, n, buf0, apebs), unique-sqns(apebs0), unique-sqns(apebs1), valid-ebatbl(apebs0, wlar, vols, vtblpnum1), valid-ebatbl(apebs1, wlar, vols, vtblpnum1), valid-eraseq(apebs0, q), valid-eraseq(apebs1, q), valid-eraseq(wlar, q), valid-eraseq(q), valid-global-sqn(apebs0, sqnum), valid-global-sqn(apebs1, sqnum), valid-peb(v, vtblpnum4, mkpeb(aehdr, avhdr, buf2, m, false)), valid-peb(v, vtblpnum4, apebs0[m0]), valid-peb(mkpeb(aehdr, avhdr, buf2, m, false)), valid-vtbl(apebs0, vols, wlar, vtblpnum1), valid-vtbl(apebs1, vols, wlar, vtblpnum1), valid-wl(apebs0, wlar), valid-wl(apebs1, wlar), v ∈ vols, vtblpnum3 + n2 ≤ LEB_SIZE, n1 + n2 ≤ # buf, m ≤ vtblpnum3 ⊦ ⟪fail_or_success#(; ; err); bitflips := ?; if err = ESUCCESS then buf0 := copy(apebs[vtblpnum0].data, vtblpnum, buf0, n0, n) else choose buf with # buf = # buf0 ∧ range=(buf, 0, buf0, 0, n0) ∧ range=(buf, n0 + n, buf0, n0 + n, # buf0 - n0 + n) in buf0 := buf; if err = ESUCCESS then {buf1 := copy(buf, n1, buf0, vtblpnum3, n2); debug#("ubi: moving data from PEB " + m0.toString); ubi_change#(v, vtblpnum4, vtblpnum3 + n2, buf1, EB_PAGE_SIZE; vols, wlar, q, bflipset, vtblpnum1, sqnum, apebs0; err)} else debug#("ubi: failed to read data from PEB " + m0.toString)⟫ ( # apebs0 = # wlar ∧ unique-sqns(apebs0) ∧ valid-global-sqn(apebs0, sqnum) ∧ valid-wl(apebs0, wlar) ∧ valid-eraseq(q) ∧ valid-eraseq(wlar, q) ∧ valid-eraseq(apebs0, q) ∧ ¬ VTBL_VOLID ∈ vols ∧ bflipset-cons(bflipset, wlar) ∧ valid-ebatbl(apebs0, wlar, vols, vtblpnum1) ∧ valid-vtbl(apebs0, vols, wlar, vtblpnum1) ∧ ubi-io-inv(apebs0)), err = ESUCCESS, m0 = vtblpnum1, n2 = 0, m0 ∈ q, VTBL_VOLID ∈ vols, vtblpnum1 ∈ q

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 32:
# apebs1 = # wlar, # apebs0 = # wlar, vols[v][vtblpnum4] = ⌜m0⌝ , apebs1[m0] = mkpeb(aehdr, avhdr, buf2, m, false), wlar[m0] = wl-entry(m1, used), err ≠ ESUCCESS, m0 ≠ vtblpnum1, n2 ≠ 0, vtblpnum4 < # vols[v], m0 < # wlar, bflipset-cons(bflipset, wlar), is-aligned(n2, EB_PAGE_SIZE), is-aligned(vtblpnum3, EB_PAGE_SIZE), ubi-io-inv(apebs1), ubi-io-inv(apebs0), ubi-io-peb-inv(mkpeb(aehdr, avhdr, buf2, m, false)), unique-sqns(apebs1), unique-sqns(apebs0), valid-ebatbl(apebs1, wlar, vols, vtblpnum1), valid-ebatbl(apebs0, wlar, vols, vtblpnum1), valid-eraseq(q), valid-eraseq(wlar, q), valid-eraseq(apebs1, q), valid-eraseq(apebs0, q), valid-global-sqn(apebs1, sqnum), valid-global-sqn(apebs0, sqnum), valid-peb(v, vtblpnum4, apebs0[m0]), valid-peb(v, vtblpnum4, mkpeb(aehdr, avhdr, buf2, m, false)), valid-peb(mkpeb(aehdr, avhdr, buf2, m, false)), valid-vtbl(apebs1, vols, wlar, vtblpnum1), valid-vtbl(apebs0, vols, wlar, vtblpnum1), valid-wl(apebs1, wlar), valid-wl(apebs0, wlar), v ∈ vols, m ≤ vtblpnum3, n1 + n2 ≤ # buf, vtblpnum3 + n2 ≤ LEB_SIZE, vtblpnum3 ≤ LEB_SIZE, m ≤ LEB_SIZE, ¬ apebs0[m0].bad, ¬ VTBL_VOLID ∈ vols, ¬ m0 ∈ q, ¬ vtblpnum1 ∈ q ⊦ ⟪fail_or_success#(; ; err); bitflips := ?; buf0 := mkbuf(vtblpnum3 + n2); if err = ESUCCESS then buf0 := copy(apebs0[m0].data, 0, buf0, 0, vtblpnum3) else {n0 := 0; n := vtblpnum3; choose buf with # buf = # buf0 ∧ range=(buf, 0, buf0, 0, n0) ∧ range=(buf, n0 + n, buf0, n0 + n, # buf0 - n0 + n) in buf0 := buf}; if err = ESUCCESS then {buf1 := copy(buf, n1, buf0, vtblpnum3, n2); debug#("ubi: moving data from PEB " + m0.toString); ubi_change#(v, vtblpnum4, vtblpnum3 + n2, buf1, EB_PAGE_SIZE; vols, wlar, q, bflipset, vtblpnum1, sqnum, apebs0; err)} else debug#("ubi: failed to read data from PEB " + m0.toString)⟫ ( # apebs0 = # wlar ∧ unique-sqns(apebs0) ∧ valid-global-sqn(apebs0, sqnum) ∧ valid-wl(apebs0, wlar) ∧ valid-eraseq(q) ∧ valid-eraseq(wlar, q) ∧ valid-eraseq(apebs0, q) ∧ ¬ VTBL_VOLID ∈ vols ∧ bflipset-cons(bflipset, wlar) ∧ valid-ebatbl(apebs0, wlar, vols, vtblpnum1) ∧ valid-vtbl(apebs0, vols, wlar, vtblpnum1) ∧ ubi-io-inv(apebs0))

Rule argument

Additional information

Used simplifier rules: ubi-io-inv-fwd: n < # apebs ⊦ apebs[n] = apeb ∧ ubi-io-inv(apebs) → ubi-io-peb-inv(apeb);%lf-used-valid-peb: ⊦ n < # wlar ∧ wlar[n] = wl-entry(m, used) ∧ apebs[n] = apeb ∧ valid-wl(apebs, wlar) → valid-peb(apeb);%lf-vtbl-info: ⊦ valid-vtbl(apebs, vols, wlar, n) ∧ valid-eraseq(wlar, q) → ¬ n ∈ q;%lf-mapped-valid-peb: ⊦ v ∈ vols ∧ m < # vols[v] ∧ vols[v][m] = ⌜n⌝ ∧ valid-ebatbl(apebs, wlar, vols, n0) ∧ valid-wl(apebs, wlar) → valid-peb(v, m, apebs[n]);%lf-mapped-info: ⊦ v ∈ vols ∧ m < # vols[v] ∧ vols[v][m] = ⌜n⌝ ∧ valid-ebatbl(apebs, wlar, vols, n0) → wlar[n].status = used ∧ n ≠ n0 ∧ n < # wlar;%⊦ valid-peb(v0, m0, apeb) → (valid-peb(v1, m1, apeb) ↔ v0 = v1 ∧ m0 = m1); (s)% ⊦ wl-entry(m, stat).status = stat; (s)%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic% ⊦ m < n → (n ≤ m ↔ false); (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m ≤ m + n; (s)% ⊦ # mkbuf(n) = n; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n + 0 = n; (s)%⊦ ubi-io-read-data-pre(n, n0, m0, n1, buf, apebs) ↔ n < # apebs ∧ ¬ apebs[n].bad ∧ n0 + n1 ≤ LEB_SIZE ∧ m0 + n1 ≤ # buf; (s)