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Proof step 98 from proof initial-ex-abstract-initial (previous step)

# buf = PEB_SIZE, m0 + 1 = # pebs, pebs[m0] = mkpeb(buf, EB_PAGE_SIZE, false), abs(subarray(pebs, 0, m0), apebs), is-encoded(echdr(n), subarray(buf, 0, EB_PAGE_SIZE)), range=(buf, EB_PAGE_SIZE, emptypeb, EB_PAGE_SIZE, LEB_SIZE + EB_PAGE_SIZE), ubi-io-initial(pebs), ubi-io-initial(apebs), EB_PAGE_SIZE ≤ PEB_SIZE ⊦ (n0 < EB_PAGE_SIZE → buf[EB_PAGE_SIZE + n0] = empty) ∧ (n1 < LEB_SIZE → buf[2 * EB_PAGE_SIZE + n1] = empty)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 99:
⊦ range=(buf, n0, buf0, n1, m) ↔ n0 + m ≤ # buf ∧ n1 + m ≤ # buf0 ∧ (∀ n. n < m → buf[n0 + n] = buf0[n1 + n])
Proof step 100:
# buf = PEB_SIZE, m0 + 1 = # pebs, pebs[m0] = mkpeb(buf, EB_PAGE_SIZE, false), abs(subarray(pebs, 0, m0), apebs), is-encoded(echdr(n), subarray(buf, 0, EB_PAGE_SIZE)), ubi-io-initial(apebs), ubi-io-initial(pebs), EB_PAGE_SIZE ≤ PEB_SIZE, EB_PAGE_SIZE + LEB_SIZE + EB_PAGE_SIZE ≤ # buf, EB_PAGE_SIZE + LEB_SIZE + EB_PAGE_SIZE ≤ # emptypeb, ∀ n. n < LEB_SIZE + EB_PAGE_SIZE → buf[EB_PAGE_SIZE + n] = (emptypeb)[EB_PAGE_SIZE + n] ⊦ (n0 < EB_PAGE_SIZE → buf[EB_PAGE_SIZE + n0] = empty) ∧ (n1 < LEB_SIZE → buf[2 * EB_PAGE_SIZE + 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] → [LEB_SIZE + EB_PAGE_SIZE, EB_PAGE_SIZE, emptypeb, EB_PAGE_SIZE, buf] flags: <all paths>

Additional information

Used terms: LEB_SIZE + EB_PAGE_SIZE, EB_PAGE_SIZE, emptypeb, EB_PAGE_SIZE, buf