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Proof step 328 from proof refine-write (previous step)

# apebs = # wlar, apebs[n4] = mkpeb(aehdr, avhdr, buf2, m0, false), wlar[n4] = wl-entry(m1, used), avols[v][vtblpnum3] = mapped(buf2, m), vols[v][vtblpnum3] = ⌜n4⌝ , n1 ≠ 0, vtblpnum4 ≠ n4, avhdr.valid?, aehdr.valid?, n4 < # wlar, vtblpnum3 < # avols[v], vtblpnum3 < # vols[v], abs(avols, apebs, vols, q), bflipset-cons(bflipset, wlar), ebm-cons(avols), is-aligned(n1, EB_PAGE_SIZE), is-aligned(vtblpnum5, EB_PAGE_SIZE), ubi-io-inv(apebs), ubi-io-peb-inv(mkpeb(aehdr, avhdr, buf2, m0, false)), unique-sqns(apebs), valid-ebatbl(apebs, wlar, vols, vtblpnum4), valid-eraseq(apebs, q), valid-eraseq(wlar, q), valid-eraseq(q), valid-global-sqn(apebs, sqnum), valid-vtbl(apebs, vols, wlar, vtblpnum4), valid-wl(apebs, wlar), v ∈ avols, v ∈ vols, m0 ≤ vtblpnum5, m ≤ vtblpnum5, n1 + n3 ≤ # buf, n3 + n1 ≤ # buf, vtblpnum5 + n1 ≤ LEB_SIZE, m0 ≤ LEB_SIZE, m ≤ LEB_SIZE, vtblpnum5 ≤ LEB_SIZE, ⌊err3⌋ , ¬ VTBL_VOLID ∈ vols ⊦ ⟪ubi_change# (v, vtblpnum3, vtblpnum5 + n1, copy(buf, n3, copy(buf2, 0, mkbuf(vtblpnum5 + n1), 0, vtblpnum5), vtblpnum5, n1), EB_PAGE_SIZE ; vols, wlar, q, bflipset, vtblpnum4, sqnum, apebs ; err0)⟫ ⟨ebm_write#(v, vtblpnum3, vtblpnum5, n3, n1, buf; avols; err1)⟩ (abs(avols, apebs, vols, q) ∧ err0 = err1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 329:
⊦ n0 + m ≤ # buf ∧ n1 + m ≤ # buf0 → copy(buf, n0, buf0, n1, m) = subarray(buf0, 0, n1) + subarray(buf, n0, m) + subarray(buf0, n1 + m, # buf0 - n1 - m)
Proof step 330:
# apebs = # wlar, vols[v][vtblpnum3] = ⌜n4⌝ , avols[v][vtblpnum3] = mapped(buf2, m), wlar[n4] = wl-entry(m1, used), apebs[n4] = mkpeb(aehdr, avhdr, buf2, m0, false), aehdr.valid?, avhdr.valid?, vtblpnum3 < # vols[v], vtblpnum3 < # avols[v], n4 < # wlar, abs(avols, apebs, vols, q), bflipset-cons(bflipset, wlar), ebm-cons(avols), is-aligned(vtblpnum5, EB_PAGE_SIZE), is-aligned(n1, EB_PAGE_SIZE), ubi-io-inv(apebs), ubi-io-peb-inv(mkpeb(aehdr, avhdr, buf2, m0, false)), unique-sqns(apebs), valid-ebatbl(apebs, wlar, vols, vtblpnum4), valid-eraseq(q), valid-eraseq(wlar, q), valid-eraseq(apebs, q), valid-global-sqn(apebs, sqnum), valid-vtbl(apebs, vols, wlar, vtblpnum4), valid-wl(apebs, wlar), v ∈ vols, v ∈ avols, vtblpnum5 ≤ LEB_SIZE, m ≤ LEB_SIZE, m0 ≤ LEB_SIZE, vtblpnum5 + n1 ≤ LEB_SIZE, n1 + n3 ≤ # buf, m ≤ vtblpnum5, m0 ≤ vtblpnum5, n3 + n1 ≤ # buf, vtblpnum5 + n1 ≤ # copy(buf2, 0, mkbuf(vtblpnum5 + n1), 0, vtblpnum5), ⌊err3⌋ ⊦ ⟪ubi_change# (v, vtblpnum3, vtblpnum5 + n1, subarray(copy(buf2, 0, mkbuf(vtblpnum5 + n1), 0, vtblpnum5), 0, vtblpnum5) + subarray(buf, n3, n1) + subarray (copy(buf2, 0, mkbuf(vtblpnum5 + n1), 0, vtblpnum5), vtblpnum5 + n1, # copy(buf2, 0, mkbuf(vtblpnum5 + n1), 0, vtblpnum5) - vtblpnum5 - n1), EB_PAGE_SIZE ; vols, wlar, q, bflipset, vtblpnum4, sqnum, apebs ; err0)⟫ ⟨ebm_write#(v, vtblpnum3, vtblpnum5, n3, n1, buf; avols; err1)⟩ (abs(avols, apebs, vols, q) ∧ err0 = err1), n1 = 0, vtblpnum4 = n4, VTBL_VOLID ∈ vols

Rule argument

spec: array-splice, inst: buffer name: copy2append seq: ⊦ n0 + m ≤ # buf ∧ n1 + m ≤ # buf0 → copy(buf, n0, buf0, n1, m) = subarray(buf0, 0, n1) + subarray(buf, n0, m) + subarray(buf0, n1 + m, # buf0 - n1 - m) subst: [m, n1, buf0, n0, buf] → [n1, vtblpnum5, copy(buf2, 0, mkbuf(vtblpnum5 + n1), 0, vtblpnum5), n3, buf] flags: <all paths>

Additional information

Used simplifier rules: ⊦ # copy(buf, m, buf0, m0, n) = # buf0; (s)% ⊦ # mkbuf(n) = n; (s)% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)% ⊦ m ≤ m; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ n + 0 = n; (s)%⊦ v ∈ avols ∧ m < # avols[v] ∧ avols[v][m] = mapped(buf, n) ∧ ebm-cons(avols) → # buf = LEB_SIZE; (s)% ⊦ m ≤ m + n; (s)% ⊦ m + n - m = n; (s)% ⊦ m - m = 0; (s)% ⊦ n ≥ m ↔ m ≤ n; (s) Used terms: n1, vtblpnum5, copy(buf2, 0, mkbuf(vtblpnum5 + n1), 0, vtblpnum5), n3, buf