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Proof step 231 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), buf0 = buf, lpt = lpt0, m = m3, m0 = EB_PAGE_SIZE, n2 = n, 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 + n ≤ LEB_SIZE, n ≤ # buf, ¬ rofs → wbuf.offset + wbuf.nbytes + n2 ≤ LEB_SIZE ∧ n2 ≤ # buf0, ¬ rofs → # buf2 = m1, rofs → m1 ≤ # buf2 ⊦ ⟪wbuf.content := copy(buf0, 0, wbuf.content, wbuf.nbytes, n2); wbuf.nbytes := wbuf.nbytes + n2; err := ESUCCESS⟫ ⟨awbuf_write_buf#(n, buf, adr0, m3, plog0, lpt0, ns0, buffered(m4); avol1, rofs0; err0)⟩ (abs(avol1, buffered(m4), wbuf, avol, rofs) ∧ (rofs0 ↔ rofs) ∧ err = err0), bleb = nobuffer, wbuf.nbytes + n2 ≥ m0

Heuristic symbolic execution applied rule assign right

And obtained the following new goals

Proof step 232:
# buf1 = EB_PAGE_SIZE, # lpt0 = # avol1, # avol0 = # avol1, rofs0 ↔ rofs, avol0[m4] = mapped(buf2), adr = adr0, avol = avol0, bleb = buffered(m4), buf0 = buf, lpt = lpt0, m = m3, m0 = EB_PAGE_SIZE, n2 = n, 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 + n2 ≤ # buf0, wbuf.nbytes + n2 ≤ # wbuf.content, n ≤ # buf, # avol1[m4].data + n ≤ LEB_SIZE, rofs → m1 ≤ # buf2, ¬ rofs → # buf2 = m1, ¬ rofs → wbuf.offset + wbuf.nbytes + n2 ≤ LEB_SIZE ∧ n2 ≤ # buf0 ⊦ ⟪wbuf := (wbuf.content:= copy(buf0, 0, wbuf.content, wbuf.nbytes, n2)) .nbytes:= ((wbuf.content:= copy(buf0, 0, wbuf.content, wbuf.nbytes, n2)).nbytes + n2); err := ESUCCESS⟫ ⟨awbuf_write_buf#(n, buf, adr0, m3, plog0, lpt0, ns0, buffered(m4); avol1, rofs0; err0)⟩ (abs(avol1, buffered(m4), wbuf, avol, rofs) ∧ (rofs0 ↔ rofs) ∧ err = err0), bleb = nobuffer, wbuf.nbytes + n2 ≥ m0

Rule argument

Additional information

Used simplifier rules: ⊦ nobuffer ≠ buffered(m); (s)% ⊦ mkwbuf(buf, m, m0).nbytes = m0; (s)% ⊦ n ≥ m ↔ m ≤ n; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ 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)%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]%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%inv-buf-in-vol: ⊦ awbuf-inv(avol, buffered(n)) → n < # avol; (forward) from specification awbuf-inv% ⊦ m < n → n ≠ 0; (s)% ⊦ m +1 = m + 1; (s)% ⊦ ¬ m + n < m; (s)