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Proof step 26 from proof prepost-write-multiple (previous step)

# apebs = # wlar, # apebs0 = # wlar0, LEB_SIZE = (n1 + m0) + m1, vols0[v][m] = unmapped, apebs1 = apebs, q1 = q, vols = vols0, m < # vols0[v], bflipset-cons(bflipset, wlar), bflipset-cons(bflipset, wlar0), id(apebs, apebs0, mapped-pebs(vols0)), is-aligned(m0, EB_PAGE_SIZE), is-aligned(m1, EB_PAGE_SIZE), ubi-io-inv(apebs0), ubi-io-inv(apebs), unique-sqns(apebs), unique-sqns(apebs0), valid-ebatbl(apebs, wlar, vols0, vtblpnum3), valid-ebatbl(apebs0, wlar0, vols0, vtblpnum3), valid-eraseq(apebs, q), valid-eraseq(wlar, q), valid-eraseq(q), valid-eraseq(q0), valid-eraseq(wlar0, q0), valid-eraseq(apebs0, q0), valid-global-sqn(apebs, sqnum), valid-global-sqn(apebs0, sqnum0), valid-vtbl(apebs, vols0, wlar, vtblpnum3), valid-vtbl(apebs0, vols0, wlar0, vtblpnum3), valid-wl(apebs, wlar), valid-wl(apebs0, wlar0), v ∈ vols0, m1 ≤ LEB_SIZE, m2 + m1 ≤ # buf, vtblpnum4 ≤ UBI_WRITE_RETRIES, m1 + m2 ≤ # buf, m0 + m1 ≤ LEB_SIZE, q.lebrefs ⊆ q0.lebrefs ++ (v × m), ⌊err⌋ , m1 = 0 → q.lebrefs ⊆ q0.lebrefs ⊦ ∀ vols, wlar, q, sqnum, apebs, err. # apebs = # wlar ∧ unique-sqns(apebs) ∧ valid-global-sqn(apebs, sqnum) ∧ 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, vtblpnum3) ∧ valid-vtbl(apebs, vols, wlar, vtblpnum3) ∧ ubi-io-inv(apebs) ∧ id(apebs, apebs1, mapped-pebs(vols0)) ∧ q.lebrefs ⊆ q1.lebrefs ++ (v × m) ∧ (m1 = 0 → q.lebrefs ⊆ q1.lebrefs) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err ≠ ESUCCESS → vols = vols0) ∧ ( err = ESUCCESS → (∃ n. vols = vols0[v, vols0[v][m, ⌜n⌝ ]] ∧ (m1 ≠ 0 → apebs[n].fill = m0 + m1) ∧ (m1 = 0 → apebs[n].fill = 0) ∧ apebs[n].data = mkempbuf(m0) + subarray(buf, m2, m1) + mkempbuf(n1))) → ⟪vtblpnum := vtblpnum4 + 1⟫ ( v ∈ vols ∧ m < # vols[v] ∧ id(apebs, apebs0, mapped-pebs(vols0)) ∧ q.lebrefs ⊆ q0.lebrefs ++ (v × m) ∧ (m1 = 0 → q.lebrefs ⊆ q0.lebrefs) ∧ (err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err ≠ ESUCCESS → vols = vols0) ∧ ( err = ESUCCESS → (∃ n. vols = vols0[v, vols0[v][m, ⌜n⌝ ]] ∧ (m1 ≠ 0 → apebs[n].fill = m0 + m1) ∧ (m1 = 0 → apebs[n].fill = 0) ∧ apebs[n].data = mkempbuf(m0) + subarray(buf, m2, m1) + mkempbuf(n1))) ∧ ¬ UBI_WRITE_RETRIES < (UBI_WRITE_RETRIES + 1 - vtblpnum) + vtblpnum4), vtblpnum3 ∈ q, vtblpnum3 ∈ q0, VTBL_VOLID ∈ vols0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 27:
# apebs = # wlar, # apebs0 = # wlar0, # apebs2 = # wlar1, LEB_SIZE = (n1 + m0) + m1, vols0[v][m] = unmapped, m < # vols0[v], bflipset-cons(bflipset, wlar), bflipset-cons(bflipset, wlar0), bflipset-cons(bflipset, wlar1), id(apebs, apebs0, mapped-pebs(vols0)), id(apebs2, apebs, mapped-pebs(vols0)), id(apebs2, apebs0, mapped-pebs(vols0)), is-aligned(m0, EB_PAGE_SIZE), is-aligned(m1, EB_PAGE_SIZE), ubi-io-inv(apebs0), ubi-io-inv(apebs), ubi-io-inv(apebs2), unique-sqns(apebs), unique-sqns(apebs0), unique-sqns(apebs2), valid-ebatbl(apebs, wlar, vols0, vtblpnum3), valid-ebatbl(apebs0, wlar0, vols0, vtblpnum3), valid-ebatbl(apebs2, wlar1, vols1, vtblpnum3), valid-eraseq(apebs, q), valid-eraseq(wlar, q), valid-eraseq(q), valid-eraseq(q0), valid-eraseq(wlar0, q0), valid-eraseq(apebs0, q0), valid-eraseq(apebs2, q2), valid-eraseq(wlar1, q2), valid-eraseq(q2), valid-global-sqn(apebs, sqnum), valid-global-sqn(apebs0, sqnum0), valid-global-sqn(apebs2, sqnum1), valid-vtbl(apebs, vols0, wlar, vtblpnum3), valid-vtbl(apebs0, vols0, wlar0, vtblpnum3), valid-vtbl(apebs2, vols1, wlar1, vtblpnum3), valid-wl(apebs, wlar), valid-wl(apebs0, wlar0), valid-wl(apebs2, wlar1), v ∈ vols0, m1 ≤ LEB_SIZE, m2 + m1 ≤ # buf, vtblpnum4 ≤ UBI_WRITE_RETRIES, m1 + m2 ≤ # buf, m0 + m1 ≤ LEB_SIZE, q.lebrefs ⊆ q0.lebrefs ++ (v × m), q2.lebrefs ⊆ q.lebrefs ++ (v × m), ⌊err⌋ , ¬ vtblpnum3 ∈ q2, ¬ VTBL_VOLID ∈ vols1, ¬ vtblpnum3 ∈ q, ¬ vtblpnum3 ∈ q0, ¬ VTBL_VOLID ∈ vols0, err0 = ESUCCESS → vols1 = vols0[v, vols0[v][m, ⌜n⌝ ]] ∧ (m1 ≠ 0 → apebs2[n].fill = m0 + m1) ∧ (m1 = 0 → apebs2[n].fill = 0) ∧ apebs2[n].data = mkempbuf(m0) + subarray(buf, m2, m1) + mkempbuf(n1), m1 = 0 → q.lebrefs ⊆ q0.lebrefs, err0 ≠ ESUCCESS → vols1 = vols0, m1 = 0 → q2.lebrefs ⊆ q.lebrefs, err0 = ESUCCESS ∨ ⌊err0⌋ ⊦ ⟪vtblpnum := vtblpnum4 + 1⟫ ( v ∈ vols1 ∧ m < # vols1[v] ∧ q2.lebrefs ⊆ q0.lebrefs ++ (v × m) ∧ (m1 = 0 → q2.lebrefs ⊆ q0.lebrefs) ∧ (err0 = ESUCCESS ∨ ⌊err0⌋ ) ∧ (err0 ≠ ESUCCESS → vols1 = vols0) ∧ ( err0 = ESUCCESS → (∃ n. vols1 = vols0[v, vols0[v][m, ⌜n⌝ ]] ∧ (m1 ≠ 0 → apebs2[n].fill = m0 + m1) ∧ (m1 = 0 → apebs2[n].fill = 0) ∧ apebs2[n].data = mkempbuf(m0) + subarray(buf, m2, m1) + mkempbuf(n1))) ∧ ¬ UBI_WRITE_RETRIES < (UBI_WRITE_RETRIES + 1 - vtblpnum) + vtblpnum4)

Rule argument

Additional information

Used simplifier rules: lf-vtbl-info: ⊦ valid-vtbl(apebs, vols, wlar, n) ∧ valid-eraseq(wlar, q) → ¬ n ∈ q;%int-c: ⊦ ns ∩ ns0 = ns0 ∩ ns; from specification set-union[nat-set]%int-a: ⊦ (ns ∩ ns0) ∩ ns1 = ns ∩ ns0 ∩ ns1; from specification set-union[nat-set]% ⊦ ns ∩ ns = ns; (s)%idset-trans-intersect: ⊦ id(apebs2, apebs1, ns0) ∧ id(apebs1, apebs0, ns1) → id(apebs2, apebs0, ns0 ∩ ns1); (forward) from specification ubi-base