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Proof step 147 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) = n0 + m2, n1 < # buf3, n1 < n0, m2 < EB_PAGE_SIZE, m4 < # avol1, n < # avol1, awbuf-inv(avol1, buffered(m4)), ebm-vol-inv(avol0), is-aligned(# buf2, EB_PAGE_SIZE), is-aligned(n0 + m2, EB_PAGE_SIZE), is-aligned(n1 + m2, EB_PAGE_SIZE), # buf2 + n0 + m2 ≤ LEB_SIZE, n0 ≤ # buf3, # buf2 + m2 + n3 ≤ LEB_SIZE, EB_PAGE_SIZE ≤ m2 + n3, n3 ≤ # buf3, # buf + n3 ≤ LEB_SIZE, ⌊err1⌋ , ∀ 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)) ⊦ n1 + m2 = 0, n3 = 0, (n ≠ m4 → avol1[n] = avol0[n]) ∧ ( n = m4 → n1 ≠ 0 ∧ buf + subarray(buf3, 0, n1) = buf2 + subarray(copy(buf3, 0, copy(buf1, 0, mkbuf(n0 + m2), 0, m2), m2, n0), 0, n1 + m2) ∧ subarray(buf1, 0, m2) = subarray(subarray(copy(buf3, 0, copy(buf1, 0, mkbuf(n0 + m2), 0, m2), m2, n0), 0, n1 + m2), 0, m2))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 148:
# buf1 = EB_PAGE_SIZE, # lpt0 = # avol1, # avol0 = # avol1, avol1[m4] = mapped(buf), avol0[m4] = mapped(buf2), align↓(m2 + n3, EB_PAGE_SIZE) = n0 + m2, n1 < # buf3, n1 < n0, m2 < EB_PAGE_SIZE, m4 < # avol1, n < # avol1, awbuf-inv(avol1, buffered(m4)), ebm-vol-inv(avol0), is-aligned(# buf2, EB_PAGE_SIZE), is-aligned(n0 + m2, EB_PAGE_SIZE), is-aligned(n1 + m2, EB_PAGE_SIZE), # buf2 + n0 + m2 ≤ LEB_SIZE, n0 ≤ # buf3, # buf2 + m2 + n3 ≤ LEB_SIZE, EB_PAGE_SIZE ≤ m2 + n3, n3 ≤ # buf3, # buf + n3 ≤ LEB_SIZE, ⌊err1⌋ , ∀ n2. n2 < # avol1 → (n2 ≠ m4 → avol1[n2] = avol0[n2]) ∧ (n2 = m4 → buf = buf2 + subarray(buf1, 0, m2)) ⊦ n1 + m2 = 0, n3 = 0, (n ≠ m4 → avol1[n] = avol0[n]) ∧ ( n = m4 → n1 ≠ 0 ∧ buf + subarray(buf3, 0, n1) = buf2 + subarray(copy(buf3, 0, copy(buf1, 0, mkbuf(n0 + m2), 0, m2), m2, n0), 0, n1 + m2) ∧ subarray(buf1, 0, m2) = subarray(subarray(copy(buf3, 0, copy(buf1, 0, mkbuf(n0 + m2), 0, m2), m2, n0), 0, n1 + m2), 0, m2))

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)