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Proof step 144 from proof refine-write-buf (previous step)

# avol0 = # avol1, # lpt0 = # avol1, # buf1 = EB_PAGE_SIZE, avol0[m4] = mapped(buf2), avol1[m4] = mapped(buf), align↓(m2 + n3, EB_PAGE_SIZE) = n0 + m2, m4 < # avol1, m2 < EB_PAGE_SIZE, n1 < n0, n1 < # buf3, abs(avol1, buffered(m4), mkwbuf(buf1, # buf2, m2), avol0, false), awbuf-inv(avol1, buffered(m4)), ebm-vol-inv(avol0), is-aligned(n1 + m2, EB_PAGE_SIZE), is-aligned(n0 + m2, EB_PAGE_SIZE), is-aligned(# buf2, EB_PAGE_SIZE), # buf + n3 ≤ LEB_SIZE, n3 ≤ # buf3, EB_PAGE_SIZE ≤ m2 + n3, # buf2 + m2 + n3 ≤ LEB_SIZE, n0 ≤ # buf3, # buf2 + n0 + m2 ≤ LEB_SIZE, ⌊err1⌋ ⊦ n1 + m2 = 0, n3 = 0, # avol1[m4, mapped(buf + subarray(buf3, 0, n1))] = # avol0[m4, mapped(buf2 + subarray(copy(buf3, 0, copy(buf1, 0, mkbuf(n0 + m2), 0, m2), m2, n0), 0, n1 + m2))] ∧ (∀ n. n < # avol1[m4, mapped(buf + subarray(buf3, 0, n1))] → ( buffered(n) ≠ buffered(m4) → avol1[m4, mapped(buf + subarray(buf3, 0, n1))][n] = avol0[m4, mapped(buf2 + subarray(copy(buf3, 0, copy(buf1, 0, mkbuf(n0 + m2), 0, m2), m2, n0), 0, n1 + m2))][n]) ∧ ( ¬ true ∧ buffered(n) = buffered(m4) → avol1[m4, mapped(buf + subarray(buf3, 0, n1))][n] = abs⊕ (avol0[m4, mapped(buf2 + subarray(copy(buf3, 0, copy(buf1, 0, mkbuf(n0 + m2), 0, m2), m2, n0), 0, n1 + m2))][n], mkwbuf(buf1, # buf2, m2))) ∧ ( true ∧ buffered(n) = buffered(m4) → mkwbuf(buf1, # buf2, m2).offset = # avol0[m4, mapped(buf2 + subarray(copy(buf3, 0, copy(buf1, 0, mkbuf(n0 + m2), 0, m2), m2, n0), 0, n1 + m2))][n].data ∧ avol1[m4, mapped(buf + subarray(buf3, 0, n1))][n] = abs⊕ (avol0[m4, mapped(buf2 + subarray(copy(buf3, 0, copy(buf1, 0, mkbuf(n0 + m2), 0, m2), m2, n0), 0, n1 + m2))][n], mkwbuf(buf1, # buf2, m2)) ∨ mkwbuf(buf1, # buf2, m2).offset < # avol0[m4, mapped(buf2 + subarray(copy(buf3, 0, copy(buf1, 0, mkbuf(n0 + m2), 0, m2), m2, n0), 0, n1 + m2))][n].data ∧ mkwbuf(buf1, # buf2, m2).offset + mkwbuf(buf1, # buf2, m2).nbytes < # avol0[m4, mapped(buf2 + subarray(copy(buf3, 0, copy(buf1, 0, mkbuf(n0 + m2), 0, m2), m2, n0), 0, n1 + m2))][n].data ∧ avol1[m4, mapped(buf + subarray(buf3, 0, n1))][n] = avol0[m4, mapped(buf2 + subarray(copy(buf3, 0, copy(buf1, 0, mkbuf(n0 + m2), 0, m2), m2, n0), 0, n1 + m2))][n] ∧ subarray(mkwbuf(buf1, # buf2, m2).content, 0, mkwbuf(buf1, # buf2, m2).nbytes) = subarray (avol0[m4, mapped(buf2 + subarray(copy(buf3, 0, copy(buf1, 0, mkbuf(n0 + m2), 0, m2), m2, n0), 0, n1 + m2))][n].data, mkwbuf(buf1, # buf2, m2).offset, mkwbuf(buf1, # buf2, m2).nbytes)))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 145:
# avol0 = # avol1, # lpt0 = # avol1, # buf1 = EB_PAGE_SIZE, avol0[m4] = mapped(buf2), avol1[m4] = mapped(buf), align↓(m2 + n3, EB_PAGE_SIZE) = n0 + m2, n < # avol1, m4 < # avol1, m2 < EB_PAGE_SIZE, n1 < n0, n1 < # buf3, abs(avol1, buffered(m4), mkwbuf(buf1, # buf2, m2), avol0, false), awbuf-inv(avol1, buffered(m4)), ebm-vol-inv(avol0), is-aligned(n1 + m2, EB_PAGE_SIZE), is-aligned(n0 + m2, EB_PAGE_SIZE), is-aligned(# buf2, EB_PAGE_SIZE), # buf + n3 ≤ LEB_SIZE, n3 ≤ # buf3, EB_PAGE_SIZE ≤ m2 + n3, # buf2 + m2 + n3 ≤ LEB_SIZE, n0 ≤ # buf3, # buf2 + n0 + m2 ≤ LEB_SIZE, ⌊err1⌋ ⊦ 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: lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%m ≤ # buf ⊦ subarray(buf0 + buf, # buf0, m) = subarray(buf, 0, m); (s)% ⊦ ¬ m + n < m; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ mkwbuf(buf, m, m0).content = buf; (s)% ⊦ mapped(buf) = mapped(buf0) ↔ buf = buf0; (s)% ⊦ m < # avol → avol[m, aleb][m] = aleb; (s)% ⊦ m + n < m + n0 ↔ n < n0; (s)% ⊦ mkwbuf(buf, m, m0).nbytes = m0; (s)% ⊦ m < m + n ↔ n ≠ 0; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m = m + n ↔ n = 0; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ # subarray(buf, m, n) = n; (s)% ⊦ #(buf + buf0) = # buf + # buf0; (s)% ⊦ mapped(buf).data = buf; (s)%m < # avol ⊦ avol[m, aleb][m] = aleb; (s)% ⊦ m < n → (n ≤ m ↔ false); (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ mkwbuf(buf, m, m0).offset = m; (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)