Proof step 52 from proof prepost-atomic-leb-change (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

• Proof step 53:

  # apebs0 = # wlar, LEB_SIZE = n2 + n0, wlar[n1] = wl-entry(m1, free), apebs0[n1] = mkpeb(aehdr, empty, mkempbuf(LEB_SIZE), 0, false), vtblpnum1 ≠ n1, aehdr.valid?, n1 < # wlar, bflipset-cons(bflipset, wlar), is-aligned(n0, EB_PAGE_SIZE), ubi-io-inv(apebs0), ubi-io-inv(apebs0[n1, mkpeb(aehdr, avidhdr(v, m0, sqnum, datasize(buf, n0), checksum(buf, datasize(buf, n0))), mkempbuf(LEB_SIZE), 0, false)]), ubi-io-inv (apebs0 [n1, mkpeb (aehdr, avidhdr(v, m0, sqnum, datasize(buf, n0), checksum(buf, datasize(buf, n0))), subarray(buf, 0, align↑(datasize(buf, n0), EB_PAGE_SIZE)) + mkempbuf(LEB_SIZE - align↑(datasize(buf, n0), EB_PAGE_SIZE)), align↑(datasize(buf, n0), EB_PAGE_SIZE), false) ]), unique-sqns(apebs0), valid-ebatbl(apebs0, wlar, vols, vtblpnum1), valid-eraseq(q), valid-eraseq(wlar, q), valid-eraseq(apebs0, q), valid-global-sqn(apebs0, sqnum), valid-vtbl(apebs0, vols, wlar, vtblpnum1), valid-wl(apebs0, wlar), n0 ≤ # buf, n0 ≤ LEB_SIZE, align↑(datasize(buf, n0), EB_PAGE_SIZE) ≤ LEB_SIZE, align↑(datasize(buf, n0), EB_PAGE_SIZE) ≤ # buf, ¬ vtblpnum1 ∈ q, ¬ VTBL_VOLID ∈ vols, v ∈ vols ∧ m0 < # vols[v] ∨ v = VTBL_VOLID ∧ m0 = VTBL_LNUM ⊦ ⟪vtblpnum0 := vtblpnum1; vols0 := vols; q0 := q; err1 := ESUCCESS; if err1 = ESUCCESS then {vtblpnum2 := n1; if v = VTBL_VOLID ∧ m0 = VTBL_LNUM then {ubi_wl_put_peb#(VTBL_VOLID × VTBL_LNUM, vtblpnum0; wlar, q); bflipset := bflipset -- vtblpnum0; vtblpnum0 := vtblpnum2} else {vtblpnum3 := m0; if vols[v][vtblpnum3] ≠ unmapped then let vtblpnum0 = vols[v][vtblpnum3].pnum in {ubi_wl_put_peb#(v × vtblpnum3, vtblpnum0; wlar, q); bflipset := bflipset -- vtblpnum0}; vols[v][vtblpnum3] := ⌜vtblpnum2⌝ }; wlar[vtblpnum2] := wl-entry(wlar[vtblpnum2].ec, used)} else ubi_wl_put_peb#(none, n1; wlar, q)⟫ ( (err1 = ESUCCESS ∨ ⌊err1⌋ ) ∧ # apebs0 = # wlar ∧ unique-sqns (apebs0 [n1, mkpeb (aehdr, avidhdr(v, m0, sqnum, datasize(buf, n0), checksum(buf, datasize(buf, n0))), subarray(buf, 0, align↑(datasize(buf, n0), EB_PAGE_SIZE)) + mkempbuf(LEB_SIZE - align↑(datasize(buf, n0), EB_PAGE_SIZE)), align↑(datasize(buf, n0), EB_PAGE_SIZE), false) ]) ∧ valid-global-sqn (apebs0 [n1, mkpeb (aehdr, avidhdr(v, m0, sqnum, datasize(buf, n0), checksum(buf, datasize(buf, n0))), subarray(buf, 0, align↑(datasize(buf, n0), EB_PAGE_SIZE)) + mkempbuf(LEB_SIZE - align↑(datasize(buf, n0), EB_PAGE_SIZE)), align↑(datasize(buf, n0), EB_PAGE_SIZE), false) ], sqnum + 1) ∧ valid-wl (apebs0 [n1, mkpeb (aehdr, avidhdr(v, m0, sqnum, datasize(buf, n0), checksum(buf, datasize(buf, n0))), subarray(buf, 0, align↑(datasize(buf, n0), EB_PAGE_SIZE)) + mkempbuf(LEB_SIZE - align↑(datasize(buf, n0), EB_PAGE_SIZE)), align↑(datasize(buf, n0), EB_PAGE_SIZE), false) ], wlar) ∧ valid-eraseq(q) ∧ valid-eraseq(wlar, q) ∧ valid-eraseq (apebs0 [n1, mkpeb (aehdr, avidhdr(v, m0, sqnum, datasize(buf, n0), checksum(buf, datasize(buf, n0))), subarray(buf, 0, align↑(datasize(buf, n0), EB_PAGE_SIZE)) + mkempbuf(LEB_SIZE - align↑(datasize(buf, n0), EB_PAGE_SIZE)), align↑(datasize(buf, n0), EB_PAGE_SIZE), false) ], q) ∧ ¬ VTBL_VOLID ∈ vols ∧ bflipset-cons(bflipset, wlar) ∧ ( v ∈ vols0 ∨ is-encoded(to-vtbl(vols0), subarray(buf, 0, LEB_SIZE)) ∧ n0 = LEB_SIZE ∨ err1 ≠ ESUCCESS → valid-ebatbl (apebs0 [n1, mkpeb (aehdr, avidhdr(v, m0, sqnum, datasize(buf, n0), checksum(buf, datasize(buf, n0))), subarray(buf, 0, align↑(datasize(buf, n0), EB_PAGE_SIZE)) + mkempbuf(LEB_SIZE - align↑(datasize(buf, n0), EB_PAGE_SIZE)), align↑(datasize(buf, n0), EB_PAGE_SIZE), false) ], wlar, vols, vtblpnum0) ∧ valid-vtbl (apebs0 [n1, mkpeb (aehdr, avidhdr(v, m0, sqnum, datasize(buf, n0), checksum(buf, datasize(buf, n0))), subarray(buf, 0, align↑(datasize(buf, n0), EB_PAGE_SIZE)) + mkempbuf(LEB_SIZE - align↑(datasize(buf, n0), EB_PAGE_SIZE)), align↑(datasize(buf, n0), EB_PAGE_SIZE), false) ], vols, wlar, vtblpnum0)) ∧ ( err1 = ESUCCESS ∧ v = VTBL_VOLID ∧ m0 = VTBL_LNUM → (∀ v0, m. ¬ v0 ∈ vols0 ∧ is-encoded(to-vtbl(vols0)[v0, m], subarray(buf, 0, LEB_SIZE)) ∧ n0 = LEB_SIZE → valid-ebatbl (apebs0 [n1, mkpeb (aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, sqnum, datasize(buf, LEB_SIZE), checksum(buf, datasize(buf, LEB_SIZE))), subarray(buf, 0, align↑(datasize(buf, LEB_SIZE), EB_PAGE_SIZE)) + mkempbuf(LEB_SIZE - align↑(datasize(buf, LEB_SIZE), EB_PAGE_SIZE)), align↑(datasize(buf, LEB_SIZE), EB_PAGE_SIZE), false) ], wlar, vols[v0, fill(mkebatbl(m), unmapped)], vtblpnum0) ∧ valid-vtbl (apebs0 [n1, mkpeb (aehdr, avidhdr(VTBL_VOLID, VTBL_LNUM, sqnum, datasize(buf, LEB_SIZE), checksum(buf, datasize(buf, LEB_SIZE))), subarray(buf, 0, align↑(datasize(buf, LEB_SIZE), EB_PAGE_SIZE)) + mkempbuf(LEB_SIZE - align↑(datasize(buf, LEB_SIZE), EB_PAGE_SIZE)), align↑(datasize(buf, LEB_SIZE), EB_PAGE_SIZE), false) ], vols[v0, fill(mkebatbl(m), unmapped)], wlar, vtblpnum0))) ∧ (err1 = ESUCCESS ∧ v ∈ vols0 ∧ vols0[v][m0] ≠ unmapped → q = q0 + eq-entry(vols0[v][m0].pnum, v × m0) ') ∧ (err1 = ESUCCESS ∧ v = VTBL_VOLID ∧ m0 = VTBL_LNUM → q = q0 + eq-entry(vtblpnum1, VTBL_VOLID × VTBL_LNUM) ') ∧ id (apebs0 [n1, mkpeb (aehdr, avidhdr(v, m0, sqnum, datasize(buf, n0), checksum(buf, datasize(buf, n0))), subarray(buf, 0, align↑(datasize(buf, n0), EB_PAGE_SIZE)) + mkempbuf(LEB_SIZE - align↑(datasize(buf, n0), EB_PAGE_SIZE)), align↑(datasize(buf, n0), EB_PAGE_SIZE), false) ], apebs0, mapped-pebs(vols0)) ∧ (v = VTBL_VOLID ∧ m0 = VTBL_LNUM ∨ err1 ≠ ESUCCESS → vols = vols0) ∧ (v ∈ vols0 ∧ err1 = ESUCCESS → vols = vols0[v, vols0[v][m0, ⌜n1⌝ ]]) ∧ ( err1 = ESUCCESS → subarray(buf, 0, align↑(datasize(buf, n0), EB_PAGE_SIZE)) + mkempbuf(LEB_SIZE - align↑(datasize(buf, n0), EB_PAGE_SIZE)) = subarray(buf, 0, n0) + mkempbuf(n2) ∧ q.lebrefs ⊆ q0.lebrefs ++ (v × m0)) ∧ (err1 ≠ ESUCCESS → q.lebrefs = q0.lebrefs)), ∃ buf0. buf = mkempbuf(n0) + buf0

Rule argument

Additional information

Used simplifier rules: lf-vtbl-info: ⊦ valid-vtbl(apebs, vols, wlar, n) ∧ valid-eraseq(wlar, q) → ¬ n ∈ q;% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).fill = m; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).data = buf; (s)%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat% ⊦ m ≤ m; (s)% ⊦ m = m + n ↔ n = 0; (s)% ⊦ m ≤ n → (n < m ↔ false); (s)% ⊦ m < n → n ≠ 0; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%⊦ apeb = apebs[n] ∧ apeb = apebs0[n] → (id○(apebs, apebs0, n) ↔ apebs = apebs0); (s)% ⊦ id○(apebs[n, apeb], apebs0, n) ↔ id○(apebs, apebs0, n); (s)% ⊦ ¬ ⌊ESUCCESS⌋ ; (s)% ⊦ # apebs[n, apeb] = # apebs; (s)%m < # apebs ⊦ apebs[m, apeb][m, apeb0] = apebs[m, apeb0]; (s)% ⊦ m < n → (n ≤ m ↔ false); (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).bad ↔ boolvar; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).vidhdr = avhdr; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).echdr = aehdr; (s)% ⊦ m < # apebs → apebs[m, apeb][m] = apeb; (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)% ⊦ n ≥ m ↔ m ≤ n; (s)