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Proof step 52 from proof inv-write (previous step)

PEB_SIZE = n0 + m1, PEB_SIZE = n3 + m2 + n1, pebs[m3] = mkpeb(buf0, m1, false), n4 < n3, m3 < # pebs, n1 < n, is-aligned(m1, EB_PAGE_SIZE), is-aligned(n1, EB_PAGE_SIZE), is-aligned(n, EB_PAGE_SIZE), is-aligned(m2, EB_PAGE_SIZE), mtd-cons(pebs), range=(buf0, m1, emptypeb, m1, n0), m1 ≤ PEB_SIZE, m2 + n1 ≤ PEB_SIZE, n2 + n ≤ # buf, m2 + n ≤ PEB_SIZE, m1 ≤ m2, n2 + n1 ≤ # buf, ⌊err0⌋ ⊦ buf0[(m2 + n1) + n4] = empty, n1 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 53:
⊦ range=(buf, n0, buf0, n1, m) ↔ n0 + m ≤ # buf ∧ n1 + m ≤ # buf0 ∧ (∀ n. n < m → buf[n0 + n] = buf0[n1 + n])
Proof step 54:
PEB_SIZE = n3 + m2 + n1, PEB_SIZE = n0 + m1, pebs[m3] = mkpeb(buf0, m1, false), n1 < n, m3 < # pebs, n4 < n3, is-aligned(m2, EB_PAGE_SIZE), is-aligned(n, EB_PAGE_SIZE), is-aligned(n1, EB_PAGE_SIZE), is-aligned(m1, EB_PAGE_SIZE), mtd-cons(pebs), n2 + n1 ≤ # buf, m1 ≤ m2, m2 + n ≤ PEB_SIZE, n2 + n ≤ # buf, m2 + n1 ≤ PEB_SIZE, m1 ≤ PEB_SIZE, m1 + n0 ≤ # buf0, m1 + n0 ≤ # emptypeb, ⌊err0⌋ , ∀ n. n < n0 → buf0[m1 + n] = (emptypeb)[m1 + n] ⊦ buf0[(m2 + n1) + n4] = empty, n1 = 0

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, m1, emptypeb, m1, buf0] flags: <all paths>

Additional information

Used terms: n0, m1, emptypeb, m1, buf0