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Proof step 26 from proof refine-write-buf (previous step)

# avol0 = # avol1, # lpt0 = # avol1, # buf1 = EB_PAGE_SIZE, rofs0 ↔ rofs, avol0[m4] = mapped(buf2), adr = adr0, avol = avol0, bleb = buffered(m4), buf = mkbuf(n1), buf0 = buf3, lpt = lpt0, m = m3, m0 = EB_PAGE_SIZE, n = (wbuf.nbytes + n2) % m0, n0 = n1 - wbuf.nbytes, n1 = align↓(wbuf.nbytes + n2, m0), n2 = n3, ns = ns0, plog = plog0, ¬ rofs, wbuf = mkwbuf(buf1, m1, m2), m2 < EB_PAGE_SIZE, m4 < # avol1, abs(avol1, buffered(m4), mkwbuf(buf1, m1, m2), avol0, rofs), awbuf-inv(avol1, buffered(m4)), ebm-vol-inv(avol0), is-aligned(m1, EB_PAGE_SIZE), 0 + n0 ≤ # buf0, wbuf.nbytes + n0 ≤ # copy(wbuf.content, 0, buf, 0, wbuf.nbytes), # avol1[m4].data + n3 ≤ LEB_SIZE, n3 ≤ # buf3, 0 + wbuf.nbytes ≤ # buf, 0 + wbuf.nbytes ≤ # wbuf.content, n1 ≥ wbuf.nbytes, wbuf.nbytes + n2 ≥ m0, ¬ rofs → wbuf.offset + wbuf.nbytes + n2 ≤ LEB_SIZE ∧ n2 ≤ # buf0, ¬ rofs → # buf2 = m1, rofs → m1 ≤ # buf2 ⊦ ⟪apersistence_io_write# (bleb.leb, wbuf.offset, 0, n1, copy(buf0, 0, copy(wbuf.content, 0, buf, 0, wbuf.nbytes), wbuf.nbytes, n0), adr, m, plog, lpt, ns; avol; err); if err = ESUCCESS then {wbuf.content := copy(buf0, n0, wbuf.content, 0, n); wbuf.offset := wbuf.offset + n1; wbuf.nbytes := n} else rofs := true⟫ ⟨awbuf_write_buf#(n3, buf3, adr0, m3, plog0, lpt0, ns0, buffered(m4); avol1, rofs0; err0)⟩ (abs(avol1, buffered(m4), wbuf, avol, rofs) ∧ (rofs0 ↔ rofs) ∧ err = err0), bleb = nobuffer, m0 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 27:
# avol0 = # avol1, # lpt0 = # avol1, # buf1 = EB_PAGE_SIZE, avol0[m4] = mapped(buf2), n3 ≠ 0, m4 < # avol1, m2 < EB_PAGE_SIZE, 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), # buf2 + m2 + n3 ≤ LEB_SIZE, align↓(m2 + n3, EB_PAGE_SIZE) ≤ # buf3 + m2, # avol1[m4].data + n3 ≤ LEB_SIZE, n3 ≤ # buf3, m2 ≤ align↓(m2 + n3, EB_PAGE_SIZE), EB_PAGE_SIZE ≤ m2 + n3 ⊦ ⟪apersistence_io_write# (buffered(m4).leb, # buf2, 0, align↓(m2 + n3, EB_PAGE_SIZE), copy(buf3, 0, copy(buf1, 0, mkbuf(align↓(m2 + n3, EB_PAGE_SIZE)), 0, m2), m2, align↓(m2 + n3, EB_PAGE_SIZE) - m2), adr0, m3, plog0, lpt0, ns0 ; avol0 ; err); wbuf := mkwbuf(buf1, # buf2, m2); rofs := false; if err = ESUCCESS then {wbuf.content := copy(buf3, align↓(m2 + n3, EB_PAGE_SIZE) - m2, wbuf.content, 0, (m2 + n3) % EB_PAGE_SIZE); wbuf.offset := wbuf.offset + align↓(m2 + n3, EB_PAGE_SIZE); wbuf.nbytes := (m2 + n3) % EB_PAGE_SIZE} else rofs := true⟫ ⟨rofs0 := false; awbuf_write_buf#(n3, buf3, adr0, m3, plog0, lpt0, ns0, buffered(m4); avol1, rofs0; err0)⟩ (abs(avol1, buffered(m4), wbuf, avol0, rofs) ∧ (rofs0 ↔ rofs) ∧ err = err0)

Rule argument

Additional information

Used simplifier rules: ⊦ m < m + n ↔ n ≠ 0; (s)% ⊦ m < n → m ≤ n; (s)% ⊦ m ≤ m + n; (s)% ⊦ m < n → n ≠ 0; (s)%inv-buf-in-vol: ⊦ awbuf-inv(avol, buffered(n)) → n < # avol; (forward) from specification awbuf-inv%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat% ⊦ mkwbuf(buf, m, m0).offset = m; (s)%n0 ≤ n ⊦ n - n0 ≤ m ↔ n ≤ m + n0; (s)% ⊦ m ≤ m; (s)% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)%n ≤ m ⊦ (m - n) + m0 ≤ n0 ↔ m + m0 ≤ n0 + n; (s)%⊦ m < EB_PAGE_SIZE ∧ EB_PAGE_SIZE ≤ n + m → (align↓(m + n, EB_PAGE_SIZE) < m ↔ false); (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ # copy(buf, m, buf0, m0, n) = # buf0; (s)% ⊦ # mkbuf(n) = n; (s)% ⊦ mkwbuf(buf, m, m0).content = buf; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n + 0 = n; (s)% ⊦ n ≥ m ↔ m ≤ n; (s)% ⊦ mkwbuf(buf, m, m0).nbytes = m0; (s)% ⊦ nobuffer ≠ buffered(m); (s)% ⊦ EB_PAGE_SIZE ≠ 0; (s)