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Proof step 69 from proof refine-write-buf (previous step)

# buf1 = EB_PAGE_SIZE, # lpt0 = # avol1, # avol0 = # avol1, avol1[m4] = mapped(buf), avol0[m4] = mapped(buf2), align↓(m2 + n3, EB_PAGE_SIZE) = n + m2, m4 < # avol1, m2 < EB_PAGE_SIZE, n0 < # avol1, awbuf-inv(avol1, buffered(m4)), ebm-vol-inv(avol0), is-aligned(# buf2, EB_PAGE_SIZE), is-aligned(n + m2, EB_PAGE_SIZE), n + (m2 + n3) % EB_PAGE_SIZE ≤ # buf3, # buf2 + n + m2 ≤ LEB_SIZE, n ≤ # buf3, # buf2 + m2 + n3 ≤ LEB_SIZE, EB_PAGE_SIZE ≤ m2 + n3, n3 ≤ # buf3, # buf + n3 ≤ LEB_SIZE, ∀ n. n < # avol1 → (buffered(n) ≠ buffered(m4) → avol1[n] = avol0[n]) ∧ (¬ false ∧ buffered(n) = buffered(m4) → avol1[n] = abs⊕(avol0[n], mkwbuf(buf1, # buf2, m2))) ∧ ( false ∧ buffered(n) = buffered(m4) → mkwbuf(buf1, # buf2, m2).offset = # avol0[n].data ∧ avol1[n] = abs⊕(avol0[n], mkwbuf(buf1, # buf2, m2)) ∨ mkwbuf(buf1, # buf2, m2).offset < # avol0[n].data ∧ mkwbuf(buf1, # buf2, m2).offset + mkwbuf(buf1, # buf2, m2).nbytes < # avol0[n].data ∧ avol1[n] = avol0[n] ∧ subarray(mkwbuf(buf1, # buf2, m2).content, 0, mkwbuf(buf1, # buf2, m2).nbytes) = subarray(avol0[n].data, mkwbuf(buf1, # buf2, m2).offset, mkwbuf(buf1, # buf2, m2).nbytes)) ⊦ n + m2 = 0, n3 = 0, (n0 ≠ m4 → avol1[n0] = avol0[n0]) ∧ ( n0 = m4 → buf + subarray(buf3, 0, n3) = (buf2 + copy(buf3, 0, copy(buf1, 0, mkbuf(n + m2), 0, m2), m2, n)) + subarray(buf3, n, (m2 + n3) % EB_PAGE_SIZE))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 70:
# buf1 = EB_PAGE_SIZE, # lpt0 = # avol1, # avol0 = # avol1, avol1[m4] = mapped(buf), avol0[m4] = mapped(buf2), align↓(m2 + n3, EB_PAGE_SIZE) = n + m2, m4 < # avol1, m2 < EB_PAGE_SIZE, n0 < # avol1, awbuf-inv(avol1, buffered(m4)), ebm-vol-inv(avol0), is-aligned(# buf2, EB_PAGE_SIZE), is-aligned(n + m2, EB_PAGE_SIZE), n + (m2 + n3) % EB_PAGE_SIZE ≤ # buf3, # buf2 + n + m2 ≤ LEB_SIZE, n ≤ # buf3, # buf2 + m2 + n3 ≤ LEB_SIZE, EB_PAGE_SIZE ≤ m2 + n3, n3 ≤ # buf3, # buf + n3 ≤ LEB_SIZE, ∀ n1. n1 < # avol1 → (n1 ≠ m4 → avol1[n1] = avol0[n1]) ∧ (n1 = m4 → buf = buf2 + subarray(buf1, 0, m2)) ⊦ n + m2 = 0, n3 = 0, (n0 ≠ m4 → avol1[n0] = avol0[n0]) ∧ ( n0 = m4 → buf + subarray(buf3, 0, n3) = (buf2 + copy(buf3, 0, copy(buf1, 0, mkbuf(n + m2), 0, m2), m2, n)) + subarray(buf3, n, (m2 + n3) % EB_PAGE_SIZE))

Rule argument

Additional information

Used simplifier rules: ⊦ mapped(buf) = mapped(buf0) ↔ buf = buf0; (s)% ⊦ mkwbuf(buf, m, m0).nbytes = m0; (s)% ⊦ mkwbuf(buf, m, m0).content = buf; (s)%⊦ abs⊕(mapped(buf), wbuf) = mapped(buf + subarray(wbuf.content, 0, wbuf.nbytes)); (s)% ⊦ buffered(m) = buffered(m0) ↔ m = m0; (s)