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Proof step 16 from proof inv-write-buf (previous step)

# buf1 = EB_PAGE_SIZE, # lpt = # avol, avol[m4] = mapped(buf2), bleb = buffered(m4), buf = mkbuf(n1), buf0 = buf3, m = m3, m0 = EB_PAGE_SIZE, n = (wbuf.nbytes + n2) % m0, n0 = n1 - wbuf.nbytes, n1 = align↓(wbuf.nbytes + n2, m0), n2 = n3, ¬ rofs, wbuf = mkwbuf(buf1, m1, m2), m4 < # avol, ebm-vol-inv(avol), wbuf-cons(mkwbuf(buf1, m1, m2), mapped(buf2), rofs), n1 ≥ wbuf.nbytes, wbuf.nbytes + n2 ≥ m0, ¬ rofs → m1 + m2 + n3 ≤ LEB_SIZE ∧ n3 ≤ # buf3 ⊦ ⟪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⟫ (# wbuf.content = EB_PAGE_SIZE ∧ m4 < # avol ∧ wbuf-cons(wbuf, avol[m4], rofs) ∧ ebm-vol-inv(avol) ∧ # lpt = # avol), m0 = 0

Heuristic symbolic execution applied rule assign right

And obtained the following new goals

Proof step 17:
# lpt = # avol, # buf1 = EB_PAGE_SIZE, avol[m4] = mapped(buf2), bleb = buffered(m4), buf = mkbuf(n1), buf0 = buf3, m = m3, m0 = EB_PAGE_SIZE, n = (wbuf.nbytes + n2) % m0, n0 = n1 - wbuf.nbytes, n1 = align↓(wbuf.nbytes + n2, m0), n2 = n3, ¬ rofs, wbuf = mkwbuf(buf1, m1, m2), m4 < # avol, ebm-vol-inv(avol), wbuf-cons(mkwbuf(buf1, m1, m2), mapped(buf2), rofs), 0 + wbuf.nbytes ≤ # wbuf.content, 0 + wbuf.nbytes ≤ # buf, wbuf.nbytes + n2 ≥ m0, n1 ≥ wbuf.nbytes, ¬ rofs → m1 + m2 + n3 ≤ LEB_SIZE ∧ n3 ≤ # buf3 ⊦ ⟪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⟫ (# wbuf.content = EB_PAGE_SIZE ∧ m4 < # avol ∧ wbuf-cons(wbuf, avol[m4], rofs) ∧ ebm-vol-inv(avol) ∧ # lpt = # avol), m0 = 0

Rule argument

Additional information

Used simplifier rules: ⊦ EB_PAGE_SIZE ≠ 0; (s)% ⊦ mkwbuf(buf, m, m0).nbytes = m0; (s)% ⊦ n ≥ m ↔ m ≤ n; (s)% ⊦ n + 0 = n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%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-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%wbuf-cons-mapped: ⊦ wbuf-cons(wbuf, aleb, boolvar) → aleb.mapped?; (forward) from specification wbuf-base%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic% ⊦ m < n → n ≠ 0; (s)%⊦ wbuf-cons(mkwbuf(buf, m0, m1), aleb, boolvar) → (EB_PAGE_SIZE < m1 ↔ false); (s)%n ≠ 0, m % n = 0 ⊦ align↓(m, n) = m; (s)% ⊦ m ≤ m + n; (s)% ⊦ mapped(buf).mapped?; (s)