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Proof step 9 from proof mtd-cons-above-fillcount-empty (previous step)

# buf = PEB_SIZE, PEB_SIZE = n0 + m, pebs[n] = mkpeb(buf, m, false), n1 < m1, n < # pebs, is-aligned(m, EB_PAGE_SIZE), range=(buf, m, emptypeb, m, n0), m0 + m1 ≤ PEB_SIZE, m ≤ m0, m ≤ PEB_SIZE ⊦ buf[m0 + n1] = empty

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ range=(buf, n0, buf0, n1, m) ↔ n0 + m ≤ # buf ∧ n1 + m ≤ # buf0 ∧ (∀ n. n < m → buf[n0 + n] = buf0[n1 + n])
Proof step 11:
# buf = PEB_SIZE, PEB_SIZE = n0 + m, pebs[n] = mkpeb(buf, m, false), n < # pebs, n1 < m1, is-aligned(m, EB_PAGE_SIZE), m ≤ PEB_SIZE, m ≤ m0, m0 + m1 ≤ PEB_SIZE, m + n0 ≤ # buf, m + n0 ≤ # emptypeb, ∀ n. n < n0 → buf[m + n] = (emptypeb)[m + n] ⊦ buf[m0 + n1] = 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, m, emptypeb, m, buf] flags: <all paths>

Additional information

Used terms: n0, m, emptypeb, m, buf