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Proof step 66 from proof inv-write (previous step)

LEB_SIZE = n4 + m1 + n1, LEB_SIZE = n0 + m, avols[v][m2] = mapped(buf0, m), m2 < # avols[v], n1 < n, ebm-cons(avols), is-aligned(n, EB_PAGE_SIZE), is-aligned(m1, EB_PAGE_SIZE), is-aligned(n1, EB_PAGE_SIZE), is-aligned(m, EB_PAGE_SIZE), range=(buf0, m, emptyleb, 0, n0), v ∈ avols, m1 + n1 ≤ LEB_SIZE, m1 ≤ LEB_SIZE, n + n2 ≤ # buf, m1 + n ≤ LEB_SIZE, n2 + n1 ≤ # buf, m ≤ LEB_SIZE, m ≤ m1, n1 + m1 ≤ LEB_SIZE, ⌊err0⌋ ⊦ n1 = 0, range=(subarray(buf0, 0, m1) + subarray(buf, n2, n1) + mkempbuf(n4), m1 + n1, emptyleb, 0, n4)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 67:
⊦ range=(buf, n0, buf0, n1, m) ↔ n0 + m ≤ # buf ∧ n1 + m ≤ # buf0 ∧ (∀ n. n < m → buf[n0 + n] = buf0[n1 + n])
Proof step 68:
LEB_SIZE = n0 + m, LEB_SIZE = n4 + m1 + n1, avols[v][m2] = mapped(buf0, m), n1 < n, m2 < # avols[v], ebm-cons(avols), is-aligned(m, EB_PAGE_SIZE), is-aligned(n1, EB_PAGE_SIZE), is-aligned(m1, EB_PAGE_SIZE), is-aligned(n, EB_PAGE_SIZE), range=(buf0, m, emptyleb, 0, n0), v ∈ avols, n1 + m1 ≤ LEB_SIZE, m ≤ m1, m ≤ LEB_SIZE, n2 + n1 ≤ # buf, m1 + n ≤ LEB_SIZE, n + n2 ≤ # buf, m1 ≤ LEB_SIZE, m1 + n1 ≤ LEB_SIZE, ⌊err0⌋ ⊦ n1 = 0, (m1 + n1) + n4 ≤ #(subarray(buf0, 0, m1) + subarray(buf, n2, n1) + mkempbuf(n4)) ∧ 0 + n4 ≤ # emptyleb ∧ (∀ n. n < n4 → (subarray(buf0, 0, m1) + subarray(buf, n2, n1) + mkempbuf(n4))[(m1 + n1) + 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] → [n4, 0, emptyleb, m1 + n1, subarray(buf0, 0, m1) + subarray(buf, n2, n1) + mkempbuf(n4)] flags: <all paths>

Additional information

Used terms: n4, 0, emptyleb, m1 + n1, subarray(buf0, 0, m1) + subarray(buf, n2, n1) + mkempbuf(n4)