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Proof step 122 from proof recovery (previous step)

# 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, n1 < n0, n1 < LEB_SIZE, 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, n0 ≤ LEB_SIZE, q0.lebrefs ⊆ q.lebrefs, avols0[v][m] = erased → ¬ v × m ∈ q ⊦ buf[m0 + n1] = empty, aehdr = empty, avhdr = empty, avols0[v][m].mapped?, VTBL_VOLID ∈ vols0, VTBL_VOLID ∈ vols

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 123:
⊦ buf = buf0 ↔ # buf = # buf0 ∧ (∀ n. n < # buf → buf[n] = buf0[n])
Proof step 124:
# subarray(buf, m0, n0) = # mkempbuf(n0), # 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, avhdr.valid?, n1 < LEB_SIZE, n1 < n0, 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, n0 ≤ LEB_SIZE, m0 ≤ LEB_SIZE, q0.lebrefs ⊆ q.lebrefs, avols0[v][m] = erased → ¬ v × m ∈ q, ∀ n. n < # subarray(buf, m0, n0) → subarray(buf, m0, n0)[n] = mkempbuf(n0)[n] ⊦ buf[m0 + n1] = empty, aehdr = empty, avhdr = empty, avols0[v][m].mapped?, VTBL_VOLID ∈ vols, VTBL_VOLID ∈ vols0

Rule argument

spec: array, inst: buffer name: Extension seq: ⊦ buf = buf0 ↔ # buf = # buf0 ∧ (∀ n. n < # buf → buf[n] = buf0[n]) subst: [buf0, buf] → [mkempbuf(n0), subarray(buf, m0, n0)] flags: <all paths>

Additional information

Used terms: mkempbuf(n0), subarray(buf, m0, n0)