Proof step 48 from proof inv-create-volume (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

• Proof step 49:

  # apebs = # wlar, # apebs0 = # wlar2, # buf0 = LEB_SIZE, wlar2[vtblpnum] = wl-entry(m, free), apebs0[vtblpnum] = mkpeb(aehdr, empty, mkempbuf(LEB_SIZE), 0, false), apebs1 = apebs0, q0 = [], vols0 = vols, vtblpnum1 = vtblpnum3, v ≠ VTBL_VOLID, vtblpnum3 ≠ vtblpnum, aehdr.valid?, vtblpnum < # wlar2, bflipset-cons(bflipset, wlar), bflipset-cons(bflipset, wlar2), id(apebs0, apebs, mapped-pebs(vols)), is-aligned(LEB_SIZE, EB_PAGE_SIZE), is-encoded(to-vtbl(vols)[v, n], buf0), ubi-io-inv(apebs), ubi-io-inv(apebs0), unique-sqns(apebs), unique-sqns(apebs0), valid-ebatbl(apebs, wlar, vols, vtblpnum3), valid-ebatbl(apebs0, wlar2, vols, vtblpnum3), valid-eraseq(q), valid-eraseq(wlar, q), valid-eraseq(apebs, q), valid-eraseq(wlar2, []), valid-global-sqn(apebs, sqnum), valid-global-sqn(apebs0, sqnum), valid-vtbl(apebs, vols, wlar, vtblpnum3), valid-vtbl(apebs0, vols, wlar2, vtblpnum3), valid-wl(apebs, wlar), valid-wl(apebs0, wlar2), 2 * ENCODED_NAT_SIZE + (ENCODED_VOLID_SIZE + ENCODED_NAT_SIZE) * # vols + ENCODED_VOLID_SIZE ≤ LEB_SIZE, # to-vtbl(vols)[v, n] * (ENCODED_NAT_SIZE + ENCODED_VOLID_SIZE) + ENCODED_NAT_SIZE ≤ LEB_SIZE, ¬ vtblpnum3 ∈ q, ¬ VTBL_VOLID ∈ vols, ¬ v ∈ vols ⊦ [ubi_atomic_leb_change#(VTBL_VOLID, VTBL_LNUM, vtblpnum, LEB_SIZE, buf0, EB_PAGE_SIZE; vols, wlar2, q0, bflipset, vtblpnum3, sqnum, apebs0; err)] ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ id○(apebs0, apebs1, vtblpnum) ∧ ubi-io-inv(apebs0) ∧ # apebs0 = # wlar2 ∧ unique-sqns(apebs0) ∧ valid-global-sqn(apebs0, sqnum) ∧ valid-wl(apebs0, wlar2) ∧ valid-eraseq(q0) ∧ valid-eraseq(wlar2, q0) ∧ valid-eraseq(apebs0, q0) ∧ ¬ VTBL_VOLID ∈ vols0 ∧ bflipset-cons(bflipset, wlar2) ∧ ( is-encoded(to-vtbl(vols0), buf0) ∨ err ≠ ESUCCESS → valid-ebatbl(apebs0, wlar2, vols0, vtblpnum3) ∧ valid-vtbl(apebs0, vols0, wlar2, vtblpnum3)) ∧ ( err = ESUCCESS → (∀ v0, m. ¬ v0 ∈ vols0 ∧ is-encoded(to-vtbl(vols0)[v0, m], buf0) → valid-ebatbl(apebs0, wlar2, vols0[v0, fill(mkebatbl(m), unmapped)], vtblpnum3) ∧ valid-vtbl(apebs0, vols0[v0, fill(mkebatbl(m), unmapped)], wlar2, vtblpnum3))) ∧ (err = ESUCCESS → q0 = eq-entry(vtblpnum1, VTBL_VOLID × VTBL_LNUM) ') ∧ id(apebs0, apebs1, mapped-pebs(vols0)) ∧ vols = vols0 ∧ ( err = ESUCCESS → apebs0[vtblpnum].fill = align↑(datasize(apebs0[vtblpnum].data, LEB_SIZE), EB_PAGE_SIZE) ∧ apebs0[vtblpnum].data = buf0 ∧ q0.lebrefs ⊆ ∅ ++ (VTBL_VOLID × VTBL_LNUM)) ∧ (err ≠ ESUCCESS → q0.lebrefs = ∅) → ⟪if err = ESUCCESS then {vols[v] := mkebatbl(n); vols[v] := fill(vols[v], unmapped)}⟫ ( ¬ VTBL_VOLID ∈ vols ∧ valid-ebatbl(apebs0, wlar2, vols, vtblpnum3) ∧ valid-vtbl(apebs0, vols, wlar2, vtblpnum3) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ id(apebs0, apebs, mapped-pebs(vols)) ∧ (err = ESUCCESS → ¬ v ∈ vols0 ∧ vols = vols0[v, fill(mkebatbl(n), unmapped)] ∧ q0.lebrefs ⊆ ∅ ++ (VTBL_VOLID × VTBL_LNUM)) ∧ (err ≠ ESUCCESS → q0.lebrefs ⊆ q.lebrefs ∧ vols = vols0)))

Rule argument

Additional information

Used simplifier rules: ⊦ [].lebrefs = ∅; (s)%a: ⊦ (q + q0) + q1 = q + q0 + q1; from specification list[erasequeue-base]% ⊦ [] + q = q; (s)% ⊦ wl-entry(m, stat).status = stat; (s)%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ buf + mkempbuf(0) = buf; (s)% ⊦ m - m = 0; (s)% ⊦ q + eqent = q + eqent '; (s)%# buf = n ⊦ subarray(buf, 0, n) = buf; (s)% ⊦ valid-eraseq(apebs, []); (s)% ⊦ valid-eraseq([]); (s)%⊦ 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)% ⊦ m ≤ m; (s)