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Proof step 43 from proof inv-write (previous step)

LEB_SIZE = n1 + m1 + n, m2 < # avols[v], ebm-cons(avols), is-aligned(m1, EB_PAGE_SIZE), is-aligned(n, EB_PAGE_SIZE), v ∈ avols, n + m1 ≤ LEB_SIZE, m1 ≤ LEB_SIZE, n2 + n ≤ # buf, m1 + n ≤ LEB_SIZE, n + n2 ≤ # buf ⊦ avols[v][m2].mapped?, range=(mkempbuf(m1) + subarray(buf, n2, n) + mkempbuf(n1), m1 + n, emptyleb, 0, n1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 44:
⊦ range=(buf, n0, buf0, n1, m) ↔ n0 + m ≤ # buf ∧ n1 + m ≤ # buf0 ∧ (∀ n. n < m → buf[n0 + n] = buf0[n1 + n])
Proof step 45:
LEB_SIZE = n1 + m1 + n, m2 < # avols[v], ebm-cons(avols), is-aligned(n, EB_PAGE_SIZE), is-aligned(m1, EB_PAGE_SIZE), v ∈ avols, n + n2 ≤ # buf, m1 + n ≤ LEB_SIZE, n2 + n ≤ # buf, m1 ≤ LEB_SIZE, n + m1 ≤ LEB_SIZE ⊦ avols[v][m2].mapped?, (m1 + n) + n1 ≤ #(mkempbuf(m1) + subarray(buf, n2, n) + mkempbuf(n1)) ∧ 0 + n1 ≤ # emptyleb ∧ (∀ n3. n3 < n1 → (mkempbuf(m1) + subarray(buf, n2, n) + mkempbuf(n1))[(m1 + n) + n3] = (emptyleb)[0 + n3])

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] → [n1, 0, emptyleb, m1 + n, mkempbuf(m1) + subarray(buf, n2, n) + mkempbuf(n1)] flags: <all paths>

Additional information

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