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Proof step 24 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), # avol1[m4].data + n3 ≤ LEB_SIZE, n3 ≤ # buf3, n1 ≥ wbuf.nbytes, wbuf.nbytes + n2 ≥ m0, ¬ rofs → wbuf.offset + wbuf.nbytes + n2 ≤ LEB_SIZE ∧ n2 ≤ # buf0, ¬ rofs → # buf2 = m1, rofs → m1 ≤ # buf2 ⊦ ⟪buf := copy(wbuf.content, 0, buf, 0, wbuf.nbytes); buf := copy(buf0, 0, buf, wbuf.nbytes, n0); apersistence_io_write#(bleb.leb, wbuf.offset, 0, n1, buf, 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 symbolic execution applied rule assign right

And obtained the following new goals

Proof step 25:
# buf1 = EB_PAGE_SIZE, # lpt0 = # avol1, # avol0 = # avol1, 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), m4 < # avol1, m2 < EB_PAGE_SIZE, 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 + wbuf.nbytes ≤ # wbuf.content, 0 + wbuf.nbytes ≤ # buf, n3 ≤ # buf3, # avol1[m4].data + n3 ≤ LEB_SIZE, wbuf.nbytes + n2 ≥ m0, n1 ≥ wbuf.nbytes, rofs → m1 ≤ # buf2, ¬ rofs → # buf2 = m1, ¬ rofs → wbuf.offset + wbuf.nbytes + n2 ≤ LEB_SIZE ∧ n2 ≤ # buf0 ⊦ ⟪buf := copy(buf0, 0, copy(wbuf.content, 0, buf, 0, wbuf.nbytes), wbuf.nbytes, n0); apersistence_io_write#(bleb.leb, wbuf.offset, 0, n1, buf, 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

Rule argument

Additional information

Used simplifier rules: ⊦ EB_PAGE_SIZE ≠ 0; (s)% ⊦ nobuffer ≠ buffered(m); (s)% ⊦ mkwbuf(buf, m, m0).nbytes = m0; (s)% ⊦ n ≥ m ↔ m ≤ n; (s)% ⊦ mkwbuf(buf, m, m0).offset = m; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n + 0 = n; (s)%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ mkwbuf(buf, m, m0).content = buf; (s)% ⊦ # mkbuf(n) = n; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%transitivity: ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward) from specification oelem[nat-set]%inv-buf-in-vol: ⊦ awbuf-inv(avol, buffered(n)) → n < # avol; (forward) from specification awbuf-inv%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic% ⊦ m < n → n ≠ 0; (s)% ⊦ m +1 = m + 1; (s)% ⊦ m < n → ¬ n < m; (s)%n ≠ 0, m % n = 0 ⊦ align↓(m, n) = m; (s)% ⊦ m ≤ m + n; (s)% ⊦ ¬ m + n < m; (s)