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Proof step 24 from proof inv-write (previous step)

LEB_SIZE = n3 + m1 + n, LEB_SIZE = n0 + m, avols[v][m2] = mapped(buf0, m), m2 < # avols[v], ebm-cons(avols), is-aligned(m, EB_PAGE_SIZE), is-aligned(m1, EB_PAGE_SIZE), is-aligned(n, EB_PAGE_SIZE), range=(buf0, m, emptyleb, 0, n0), v ∈ avols, m ≤ LEB_SIZE, m1 ≤ LEB_SIZE, n2 + n ≤ # buf, m1 + n ≤ LEB_SIZE, n + n2 ≤ # buf, m ≤ m1, n + m1 ≤ LEB_SIZE ⊦ n = 0, range=(subarray(buf0, 0, m1) + subarray(buf, n2, n) + mkempbuf(n3), m1 + n, emptyleb, 0, n3)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 25:
⊦ range=(buf, n0, buf0, n1, m) ↔ n0 + m ≤ # buf ∧ n1 + m ≤ # buf0 ∧ (∀ n. n < m → buf[n0 + n] = buf0[n1 + n])
Proof step 26:
LEB_SIZE = n0 + m, LEB_SIZE = n3 + m1 + n, avols[v][m2] = mapped(buf0, m), m2 < # avols[v], ebm-cons(avols), is-aligned(n, EB_PAGE_SIZE), is-aligned(m1, EB_PAGE_SIZE), is-aligned(m, EB_PAGE_SIZE), range=(buf0, m, emptyleb, 0, n0), v ∈ avols, n + m1 ≤ LEB_SIZE, m ≤ m1, n + n2 ≤ # buf, m1 + n ≤ LEB_SIZE, n2 + n ≤ # buf, m1 ≤ LEB_SIZE, m ≤ LEB_SIZE ⊦ n = 0, (m1 + n) + n3 ≤ #(subarray(buf0, 0, m1) + subarray(buf, n2, n) + mkempbuf(n3)) ∧ 0 + n3 ≤ # emptyleb ∧ (∀ n4. n4 < n3 → (subarray(buf0, 0, m1) + subarray(buf, n2, n) + mkempbuf(n3))[(m1 + n) + n4] = (emptyleb)[0 + n4])

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] → [n3, 0, emptyleb, m1 + n, subarray(buf0, 0, m1) + subarray(buf, n2, n) + mkempbuf(n3)] flags: <all paths>

Additional information

Used terms: n3, 0, emptyleb, m1 + n, subarray(buf0, 0, m1) + subarray(buf, n2, n) + mkempbuf(n3)