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Proof step 122 from proof prepost-erase-worker-helper (previous step)

# apebs0 = # wlar0, wlar0[m] = wl-entry(m0, erasing), apebs1 = apebs0, err0 = EIO, vtblpnum0 = m, vtblpnum3 = 0, wlar1 = wlar0, m < # wlar0, bflipset-cons(bflipset, wlar0), erase-worker-inv(apebs0, wlar0, vtblpnum, err, apebs, vols, wlar, q0, eq-entry(m, lref), q1, bflipset, vtblpnum1, sqnum), ubi-io-inv(apebs0), unique-sqns(apebs0), valid-ebatbl(apebs0, wlar0, vols, vtblpnum1), valid-eraseq(apebs0, q0 + eq-entry(m, lref) ' + q1), valid-eraseq(wlar0, q0 + eq-entry(m, lref) ' + q1), valid-eraseq(q0 + eq-entry(m, lref) ' + q1), valid-global-sqn(apebs0, sqnum), valid-vtbl(apebs0, vols, wlar0, vtblpnum1), valid-wl(apebs0, wlar0) ⊦ ⟪aubi_io_markbad#(vtblpnum0; apebs; err); if err = ESUCCESS then wlar[vtblpnum0] := wl-entry(wlar[vtblpnum0].ec, erroneous) else debug#("ubi: marking PEB " + vtblpnum0.toString + " as bad failed")⟫ ( ( err = ESUCCESS → # apebs = # wlar ∧ unique-sqns(apebs) ∧ valid-global-sqn(apebs, sqnum) ∧ valid-wl(apebs, wlar) ∧ valid-eraseq(wlar, q0 + q1) ∧ valid-eraseq(apebs, q0 + q1) ∧ bflipset-cons(bflipset, wlar) ∧ valid-ebatbl(apebs, wlar, vols, vtblpnum1) ∧ valid-vtbl(apebs, vols, wlar, vtblpnum1)) ∧ ( err ≠ ESUCCESS → # apebs = # wlar ∧ unique-sqns(apebs) ∧ valid-global-sqn(apebs, sqnum) ∧ valid-wl(apebs, wlar) ∧ valid-eraseq(wlar, q0 + eq-entry(m, lref) ' + q1) ∧ valid-eraseq(apebs, q0 + eq-entry(m, lref) ' + q1) ∧ bflipset-cons(bflipset, wlar) ∧ valid-ebatbl(apebs, wlar, vols, vtblpnum1) ∧ valid-vtbl(apebs, vols, wlar, vtblpnum1)) ∧ ubi-io-inv(apebs) ∧ wlar[m].status ≠ used ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ id○(wlar, wlar0, m) ∧ id○(apebs, apebs0, m) ∧ id(apebs, apebs0, mapped-pebs(vols))), err = ESUCCESS, vtblpnum1 = m, vtblpnum1 ∈ q1, vtblpnum1 ∈ q0, VTBL_VOLID ∈ vols, err ≠ ESUCCESS ∧ vtblpnum ≤ UBI_ERASE_RETRIES

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 123:
# apebs0 = # wlar0, # apebs = # wlar0, # wlar = # wlar0, wlar[m].status = erasing, wlar0[m] = wl-entry(m0, erasing), err ≠ ESUCCESS, vtblpnum1 ≠ m, m < # wlar0, bflipset-cons(bflipset, wlar), bflipset-cons(bflipset, wlar0), id○(apebs, apebs0, m), id○(wlar, wlar0, m), ubi-io-inv(apebs), ubi-io-inv(apebs0), unique-sqns(apebs), unique-sqns(apebs0), valid-ebatbl(apebs, wlar, vols, vtblpnum1), valid-ebatbl(apebs0, wlar0, vols, vtblpnum1), valid-eraseq(wlar, q0 + eq-entry(m, lref) ' + q1), valid-eraseq(apebs, q0 + eq-entry(m, lref) ' + q1), valid-eraseq(q0 + eq-entry(m, lref) ' + q1), valid-eraseq(wlar0, q0 + eq-entry(m, lref) ' + q1), valid-eraseq(apebs0, q0 + eq-entry(m, lref) ' + q1), valid-global-sqn(apebs, sqnum), valid-global-sqn(apebs0, sqnum), valid-vtbl(apebs, vols, wlar, vtblpnum1), valid-vtbl(apebs0, vols, wlar0, vtblpnum1), valid-wl(apebs, wlar), valid-wl(apebs0, wlar0), ¬ VTBL_VOLID ∈ vols, ¬ vtblpnum1 ∈ q0, ¬ vtblpnum1 ∈ q1 ⊦ ⟪aubi_io_markbad#(m; apebs; err); if err = ESUCCESS then wlar[m] := wl-entry(wlar[m].ec, erroneous) else debug#("ubi: marking PEB " + m.toString + " as bad failed")⟫ ( ( err = ESUCCESS → # apebs = # wlar ∧ unique-sqns(apebs) ∧ valid-global-sqn(apebs, sqnum) ∧ valid-wl(apebs, wlar) ∧ valid-eraseq(wlar, q0 + q1) ∧ valid-eraseq(apebs, q0 + q1) ∧ bflipset-cons(bflipset, wlar) ∧ valid-ebatbl(apebs, wlar, vols, vtblpnum1) ∧ valid-vtbl(apebs, vols, wlar, vtblpnum1)) ∧ ( err ≠ ESUCCESS → # apebs = # wlar ∧ unique-sqns(apebs) ∧ valid-global-sqn(apebs, sqnum) ∧ valid-wl(apebs, wlar) ∧ valid-eraseq(wlar, q0 + eq-entry(m, lref) ' + q1) ∧ valid-eraseq(apebs, q0 + eq-entry(m, lref) ' + q1) ∧ bflipset-cons(bflipset, wlar) ∧ valid-ebatbl(apebs, wlar, vols, vtblpnum1) ∧ valid-vtbl(apebs, vols, wlar, vtblpnum1)) ∧ ubi-io-inv(apebs) ∧ wlar[m].status ≠ used ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ id○(wlar, wlar0, m) ∧ id○(apebs, apebs0, m) ∧ id(apebs, apebs0, mapped-pebs(vols)))

Rule argument

Additional information

Used simplifier rules: lf-valid-eraseq-middle-wlar: ⊦ valid-eraseq(wlar, q0 + eq-entry(m, lref) ' + q1) → m < # wlar;% ⊦ ¬ n < n; (s)% ⊦ m < n + 1 ↔ ¬ n < m; (s)% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)% ⊦ m < n → n ≠ 0; (s)% ⊦ m + 1 ≠ 0; (s)%idexcept-size: ⊦ id○(apebs, apebs0, n) → # apebs = # apebs0; (forward) from specification array-copy[apebs]%idexcept-size: ⊦ id○(wlar, wlar0, n) → # wlar = # wlar0; (forward) from specification array-copy[wlarray-base]%valid-eraseqp-in0: ⊦ valid-eraseq(wlar, q0 + eq-entry(n, lref) ' + q1) → wlar[n].status = erasing; (forward) from specification ubi-base%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%eqle-one: ⊦ m = n + 1 ∧ n < n0 → m ≤ n0; (forward) from specification nat%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m < n → (n ≤ m + 1 ↔ n = m + 1); (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)%⊦ ubi-cons(apebs, vols, wlar, q, bflipset, n0, n1) ↔ # 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(bflipset, wlar) ∧ valid-ebatbl(apebs, wlar, vols, n0) ∧ valid-vtbl(apebs, vols, wlar, n0); (s)%a: ⊦ (q + q0) + q1 = q + q0 + q1; from specification list[erasequeue-base]% ⊦ eqent + q = eqent ' + q; (s)% ⊦ eq-entry(m, lref).pnum = m; (s)%⊦ erase-worker-inv (apebs0, wlar0, m, err, apebs, vols, wlar, q0, eqent, q1, bflipset, n0, n1) ↔ m ≤ UBI_ERASE_RETRIES + 1 ∧ eqent.pnum < # apebs ∧ id○(apebs, apebs0, eqent.pnum) ∧ id○(wlar, wlar0, eqent.pnum) ∧ ubi-cons(apebs, vols, wlar, q0 + (eqent + q1), bflipset, n0, n1) ∧ ubi-io-inv(apebs) ∧ ( err = ESUCCESS → apebs[eqent.pnum].echdr = aechdr(wlar[eqent.pnum].ec) ∧ apebs[eqent.pnum].vidhdr = empty ∧ ¬ apebs[eqent.pnum].bad); (s)