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Proof step 252 from proof refine-write-buf (previous step)

# avol0 = # avol1, # lpt0 = # avol1, # buf1 = EB_PAGE_SIZE, avol0[m4] = mapped(buf2), avol1[m4] = mapped(buf0), m2 < EB_PAGE_SIZE, m2 + n < EB_PAGE_SIZE, m4 < # avol1, abs(avol1, buffered(m4), mkwbuf(buf1, # buf2, m2), avol0, false), awbuf-inv(avol1, buffered(m4)), ebm-vol-inv(avol0), is-aligned(# buf2, EB_PAGE_SIZE), # buf0 + n ≤ LEB_SIZE, n ≤ # buf, # buf2 + m2 + n ≤ LEB_SIZE ⊦ # avol1[m4, mapped(buf0 + subarray(buf, 0, n))] = # avol0 ∧ (∀ n0. n0 < # avol1[m4, mapped(buf0 + subarray(buf, 0, n))] → (buffered(n0) ≠ buffered(m4) → avol1[m4, mapped(buf0 + subarray(buf, 0, n))][n0] = avol0[n0]) ∧ ( ¬ false ∧ buffered(n0) = buffered(m4) → avol1[m4, mapped(buf0 + subarray(buf, 0, n))][n0] = abs⊕(avol0[n0], mkwbuf(copy(buf, 0, buf1, m2, n), # buf2, m2 + n))) ∧ ( false ∧ buffered(n0) = buffered(m4) → mkwbuf(copy(buf, 0, buf1, m2, n), # buf2, m2 + n).offset = # avol0[n0].data ∧ avol1[m4, mapped(buf0 + subarray(buf, 0, n))][n0] = abs⊕(avol0[n0], mkwbuf(copy(buf, 0, buf1, m2, n), # buf2, m2 + n)) ∨ mkwbuf(copy(buf, 0, buf1, m2, n), # buf2, m2 + n).offset < # avol0[n0].data ∧ mkwbuf(copy(buf, 0, buf1, m2, n), # buf2, m2 + n).offset + mkwbuf(copy(buf, 0, buf1, m2, n), # buf2, m2 + n).nbytes < # avol0[n0].data ∧ avol1[m4, mapped(buf0 + subarray(buf, 0, n))][n0] = avol0[n0] ∧ subarray (mkwbuf(copy(buf, 0, buf1, m2, n), # buf2, m2 + n).content, 0, mkwbuf(copy(buf, 0, buf1, m2, n), # buf2, m2 + n).nbytes) = subarray (avol0[n0].data, mkwbuf(copy(buf, 0, buf1, m2, n), # buf2, m2 + n).offset, mkwbuf(copy(buf, 0, buf1, m2, n), # buf2, m2 + n).nbytes)))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 253:
# avol0 = # avol1, # lpt0 = # avol1, # buf1 = EB_PAGE_SIZE, avol0[m4] = mapped(buf2), avol1[m4] = mapped(buf0), n0 < # avol1, m2 < EB_PAGE_SIZE, m2 + n < EB_PAGE_SIZE, m4 < # avol1, abs(avol1, buffered(m4), mkwbuf(buf1, # buf2, m2), avol0, false), awbuf-inv(avol1, buffered(m4)), ebm-vol-inv(avol0), is-aligned(# buf2, EB_PAGE_SIZE), # buf0 + n ≤ LEB_SIZE, n ≤ # buf, # buf2 + m2 + n ≤ LEB_SIZE ⊦ (n0 ≠ m4 → avol1[n0] = avol0[n0]) ∧ (n0 = m4 → buf0 + subarray(buf, 0, n) = buf2 + subarray(copy(buf, 0, buf1, m2, n), 0, m2 + n))

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)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic% ⊦ m < # avol → avol[m, aleb][m] = aleb; (s)% ⊦ m ≠ n → avol[n, aleb][m] = avol[m]; (s)% ⊦ buffered(m) = buffered(m0) ↔ m = m0; (s)% ⊦ abs(avol0, bleb, wbuf, avol1, rofs) → (# avol1 = # avol0 ↔ true); (ss)% ⊦ # avol[n, aleb] = # avol; (s)