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Proof step 15 from proof ebm-cons-above-fillcount (previous step)

# buf = LEB_SIZE, LEB_SIZE = n0 + m0, avols[v][m] = mapped(buf, m0), m1 < n0, m < # avols[v], is-aligned(m0, EB_PAGE_SIZE), range=(buf, m0, emptyleb, 0, n0), v ∈ avols, m0 ≤ LEB_SIZE ⊦ buf[m1 + m0] = empty

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 16:
⊦ range=(buf, n0, buf0, n1, m) ↔ n0 + m ≤ # buf ∧ n1 + m ≤ # buf0 ∧ (∀ n. n < m → buf[n0 + n] = buf0[n1 + n])
Proof step 17:
# buf = LEB_SIZE, LEB_SIZE = n0 + m0, avols[v][m] = mapped(buf, m0), m < # avols[v], m1 < n0, is-aligned(m0, EB_PAGE_SIZE), v ∈ avols, m0 ≤ LEB_SIZE, m0 + n0 ≤ # buf, 0 + n0 ≤ # emptyleb, ∀ n. n < n0 → buf[m0 + n] = (emptyleb)[0 + n] ⊦ buf[m1 + m0] = empty

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] → [n0, 0, emptyleb, m0, buf] flags: <all paths>

Additional information

Used terms: n0, 0, emptyleb, m0, buf