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Proof step 322 from proof refine-read-buf (previous step)

# buf2 = EB_PAGE_SIZE, # lpt0 = # avol1, # avol0 = # avol1, LEB_SIZE = n0 + # buf, LEB_SIZE = n1 + # buf1, avol0[n2] = mapped(buf), avol1[n2] = mapped(buf1), n2 < # avol1, m4 < EB_PAGE_SIZE, awbuf-inv(avol1, buffered(n2)), ebm-vol-inv(avol0), is-aligned(m6, EB_PAGE_SIZE), m0 + n ≤ LEB_SIZE, # buf ≤ LEB_SIZE, n ≤ # buf3, # buf1 ≤ LEB_SIZE, rofs → m6 = # buf ∧ buf1 = buf + subarray(buf2, 0, m4) ∨ m6 < # buf ∧ m6 + m4 < # buf ∧ buf1 = buf ∧ subarray(buf2, 0, m4) = subarray(buf, m6, m4), ¬ rofs → buf1 = buf + subarray(buf2, 0, m4), rofs → m6 ≤ # buf, ¬ rofs → # buf = m6 ⊦ copy(buf + mkempbuf(n0), m0, buf3, 0, n) = copy(buf1 + mkempbuf(n1), m0, buf3, 0, n), m0 ≤ m6 + m4 ∧ m6 ≤ m0 + n

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 323:
⊦ buf = buf0 ↔ # buf = # buf0 ∧ (∀ n. n < # buf → buf[n] = buf0[n])
Proof step 324:
# avol0 = # avol1, # lpt0 = # avol1, # buf2 = EB_PAGE_SIZE, LEB_SIZE = n1 + # buf1, LEB_SIZE = n0 + # buf, avol1[n2] = mapped(buf1), avol0[n2] = mapped(buf), m4 < EB_PAGE_SIZE, n2 < # avol1, awbuf-inv(avol1, buffered(n2)), ebm-vol-inv(avol0), is-aligned(m6, EB_PAGE_SIZE), # buf1 ≤ LEB_SIZE, n ≤ # buf3, # buf ≤ LEB_SIZE, m0 + n ≤ LEB_SIZE, ¬ rofs → # buf = m6, rofs → m6 ≤ # buf, ¬ rofs → buf1 = buf + subarray(buf2, 0, m4), rofs → m6 = # buf ∧ buf1 = buf + subarray(buf2, 0, m4) ∨ m6 < # buf ∧ m6 + m4 < # buf ∧ buf1 = buf ∧ subarray(buf2, 0, m4) = subarray(buf, m6, m4) ⊦ m0 ≤ m6 + m4 ∧ m6 ≤ m0 + n, # copy(buf + mkempbuf(n0), m0, buf3, 0, n) = # copy(buf1 + mkempbuf(n1), m0, buf3, 0, n) ∧ (∀ n2. n2 < # copy(buf + mkempbuf(n0), m0, buf3, 0, n) → copy(buf + mkempbuf(n0), m0, buf3, 0, n)[n2] = copy(buf1 + mkempbuf(n1), m0, buf3, 0, n)[n2])

Rule argument

spec: array, inst: buffer name: Extension seq: ⊦ buf = buf0 ↔ # buf = # buf0 ∧ (∀ n. n < # buf → buf[n] = buf0[n]) subst: [buf0, buf] → [copy(buf1 + mkempbuf(n1), m0, buf3, 0, n), copy(buf + mkempbuf(n0), m0, buf3, 0, n)] flags: <all paths>

Additional information

Used terms: copy(buf1 + mkempbuf(n1), m0, buf3, 0, n), copy(buf + mkempbuf(n0), m0, buf3, 0, n)