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Proof step 119 from proof recovery (previous step)

# wlar = # wlar0, # apebs0 = # wlar0, # avols0[v] = # vols0[v], # vols[v] = # vols0[v], LEB_SIZE = n0 + m0, vols0[v][m] = ⌜n⌝ , apebs0[n] = mkpeb(aehdr, avhdr, buf, m0, false), apebs0[unmapped.pnum] = mkpeb(aehdr0, avhdr0, buf0, m1, boolvar), vols[v][m] = unmapped, subarray(buf, m0, n0) = mkempbuf(n0), avhdr.valid?, n < # wlar0, m < # vols0[v], bflipset-cons(bflipset0, wlar0), bflipset-cons(bflipset, wlar), is-aligned(m0, EB_PAGE_SIZE), is-max(apebs0, vols0, wlar0, q0, bflipset0, vtblpnum3, sqnum), ubi-io-inv(apebs0), unique-sqns(apebs0), valid-ebatbl(apebs0, wlar0, vols0, vtblpnum3), valid-ebatbl(apebs0, wlar, vols, vtblpnum), valid-eraseq(apebs0, q0), valid-eraseq(wlar0, q0), valid-eraseq(q0), valid-eraseq(apebs0, q), valid-eraseq(wlar, q), valid-eraseq(q), valid-global-sqn(apebs0, sqnum), valid-global-sqn(apebs0, vtblpnum0), valid-vtbl(apebs0, vols0, wlar0, vtblpnum3), valid-vtbl(apebs0, vols, wlar, vtblpnum), valid-wl(apebs0, wlar0), valid-wl(apebs0, wlar), v ∈ vols0, v ∈ vols, v ∈ avols0, eq-entry(n, v × m) ∈ q, m0 ≤ LEB_SIZE, q0.lebrefs ⊆ q.lebrefs, avols0[v][m] = erased → ¬ v × m ∈ q ⊦ aehdr = empty, avhdr = empty, avols0[v][m].mapped?, range=(buf, m0, emptyleb, 0, n0), VTBL_VOLID ∈ vols, VTBL_VOLID ∈ vols0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 120:
⊦ range=(buf, n0, buf0, n1, m) ↔ n0 + m ≤ # buf ∧ n1 + m ≤ # buf0 ∧ (∀ n. n < m → buf[n0 + n] = buf0[n1 + n])
Proof step 121:
# vols[v] = # vols0[v], # avols0[v] = # vols0[v], # apebs0 = # wlar0, # wlar = # wlar0, LEB_SIZE = n0 + m0, vols[v][m] = unmapped, apebs0[unmapped.pnum] = mkpeb(aehdr0, avhdr0, buf0, m1, boolvar), apebs0[n] = mkpeb(aehdr, avhdr, buf, m0, false), vols0[v][m] = ⌜n⌝ , subarray(buf, m0, n0) = mkempbuf(n0), avhdr.valid?, m < # vols0[v], n < # wlar0, bflipset-cons(bflipset, wlar), bflipset-cons(bflipset0, wlar0), is-aligned(m0, EB_PAGE_SIZE), is-max(apebs0, vols0, wlar0, q0, bflipset0, vtblpnum3, sqnum), ubi-io-inv(apebs0), unique-sqns(apebs0), valid-ebatbl(apebs0, wlar, vols, vtblpnum), valid-ebatbl(apebs0, wlar0, vols0, vtblpnum3), valid-eraseq(q), valid-eraseq(wlar, q), valid-eraseq(apebs0, q), valid-eraseq(q0), valid-eraseq(wlar0, q0), valid-eraseq(apebs0, q0), valid-global-sqn(apebs0, vtblpnum0), valid-global-sqn(apebs0, sqnum), valid-vtbl(apebs0, vols, wlar, vtblpnum), valid-vtbl(apebs0, vols0, wlar0, vtblpnum3), valid-wl(apebs0, wlar), valid-wl(apebs0, wlar0), eq-entry(n, v × m) ∈ q, v ∈ avols0, v ∈ vols, v ∈ vols0, m0 ≤ LEB_SIZE, q0.lebrefs ⊆ q.lebrefs, avols0[v][m] = erased → ¬ v × m ∈ q ⊦ aehdr = empty, avhdr = empty, avols0[v][m].mapped?, VTBL_VOLID ∈ vols0, VTBL_VOLID ∈ vols, m0 + n0 ≤ # buf ∧ 0 + n0 ≤ # emptyleb ∧ (∀ n. n < n0 → buf[m0 + n] = (emptyleb)[0 + n])

Rule argument

spec: array-splice, inst: buffer name: range-eq-ext seq: ⊦ range=(buf, n0, buf0, n1, m) ↔ n0 + m ≤ # buf ∧ n1 + m ≤ # buf0 ∧ (∀ n. n < m → buf[n0 + n] = buf0[n1 + n]) subst: [m, n1, buf0, n0, buf] → [n0, 0, emptyleb, m0, buf] flags: <all paths>

Additional information

Used terms: n0, 0, emptyleb, m0, buf