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Proof step 10 from proof prepost-erase-worker-helper (previous step)

# apebs0 = # wlar0, wlar0[m] = wl-entry(m0, erasing), apebs = apebs0, err = EIO, vtblpnum = 0, vtblpnum0 = m, wlar = wlar0, vtblpnum1 ≠ m, m < # wlar0, bflipset-cons(bflipset, wlar0), 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), ¬ VTBL_VOLID ∈ vols, ¬ vtblpnum1 ∈ q0, ¬ vtblpnum1 ∈ q1 ⊦ ⟪while err ≠ ESUCCESS ∧ vtblpnum ≤ UBI_ERASE_RETRIES do {wlar[vtblpnum0].ec := wlar[vtblpnum0].ec + 1; aubi_io_sync_erase#(vtblpnum0; apebs; err); if err = ESUCCESS then aubi_io_write_echdr#(vtblpnum0, aechdr(wlar[vtblpnum0].ec); apebs; err) else debug#("ubi: erase of PEB " + vtblpnum0.toString + " failed"); vtblpnum := vtblpnum + 1}; if err = ESUCCESS then wlar[vtblpnum0] := wl-entry(wlar[vtblpnum0].ec, free) else {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)))

User applied rule invariant right

And obtained the following new goals

Rule argument

bound: UBI_ERASE_RETRIES + 1 - vtblpnum inv: erase-worker-inv (apebs0, wlar0, vtblpnum, err, apebs, vols, wlar, q0, eq-entry(m, lref), q1, bflipset, vtblpnum1, sqnum) fmapos: right 1

Additional information

Used simplifier rules: ⊦ 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)% ⊦ 0 ≤ m; (s)% ⊦ eq-entry(m, lref).pnum = m; (s)% ⊦ id○(apebs, apebs, n); (ss)%⊦ wle = wlar[n] ∧ wle = wlar0[n] → (id○(wlar, wlar0, n) ↔ wlar = wlar0); (s)% ⊦ eqent + q = eqent ' + q; (s)%a: ⊦ (q + q0) + q1 = q + q0 + q1; from specification list[erasequeue-base]%⊦ 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)% ⊦ ESUCCESS ≠ EIO; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat% ⊦ ¬ n < n; (s) Used formulas: erase-worker-inv (apebs0, wlar0, vtblpnum, err, apebs, vols, wlar, q0, eq-entry(m, lref), q1, bflipset, vtblpnum1, sqnum), UBI_ERASE_RETRIES + 1 - vtblpnum = UBI_ERASE_RETRIES + 1 - vtblpnum