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Proof step 57 from proof inv-write-buf (previous step)

# lpt = # avol[m1, mapped(avol[m1].data + mkempbuf(m0 - # avol[m1].data) + subarray(buf2, n1, n))], # buf1 = EB_PAGE_SIZE, # lpt = # avol, rofs ↔ false, avol[m4] = mapped(buf), buf2 = copy(buf3, 0, copy(buf1, 0, mkbuf(align↓(m2 + n3, EB_PAGE_SIZE)), 0, m2), m2, align↓(m2 + n3, EB_PAGE_SIZE) - m2), err = err0, m0 = m3, m1 = buffered(m4).leb, n0 = align↓(m2 + n3, EB_PAGE_SIZE), n1 = 0, wbuf = mkwbuf(buf1, m3, m2), buffered(m4).isbuf?, avol[m1].mapped?, m1 < # avol, n < n0, m4 < # avol, ebm-vol-inv(avol[m1, mapped(avol[m1].data + mkempbuf(m0 - # avol[m1].data) + subarray(buf2, n1, n))]), ebm-vol-inv(avol), is-aligned(n, EB_PAGE_SIZE), is-aligned(m3, EB_PAGE_SIZE), wbuf-cons(mkwbuf(buf1, m3, m2), mapped(buf), false), n1 + n ≤ # buf2, 0 + m2 ≤ # mkbuf(align↓(m2 + n3, EB_PAGE_SIZE)), 0 + m2 ≤ # buf1, m2 + (align↓(m2 + n3, EB_PAGE_SIZE) - m2) ≤ # copy(buf1, 0, mkbuf(align↓(m2 + n3, EB_PAGE_SIZE)), 0, m2), 0 + (align↓(m2 + n3, EB_PAGE_SIZE) - m2) ≤ # buf3, EB_PAGE_SIZE ≤ m2 + n3, m2 ≤ align↓(m2 + n3, EB_PAGE_SIZE), m2 ≤ EB_PAGE_SIZE, align↓(m2 + n3, EB_PAGE_SIZE) ≤ # buf3 + m2, m3 + m2 + n3 ≤ LEB_SIZE, n3 ≤ # buf3, # buf ≤ m3, m3 + align↓(m2 + n3, EB_PAGE_SIZE) ≤ LEB_SIZE, m0 ≥ # avol[m1].data, align↓(m2 + n3, EB_PAGE_SIZE) ≥ m2, ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ err = ESUCCESS, n = 0, # wbuf.content = EB_PAGE_SIZE ∧ m4 < # avol[m1, mapped(avol[m1].data + mkempbuf(m0 - # avol[m1].data) + subarray(buf2, n1, n))] ∧ wbuf-cons(wbuf, avol[m1, mapped(avol[m1].data + mkempbuf(m0 - # avol[m1].data) + subarray(buf2, n1, n))][m4], true)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 58:
# lpt = # avol, # buf1 = EB_PAGE_SIZE, avol[m4] = mapped(buf), n < align↓(m2 + n3, EB_PAGE_SIZE), m4 < # avol, n < # buf3 + m2, n < m2 + n3, ebm-vol-inv(avol), ebm-vol-inv (avol [m4, mapped ( buf + mkempbuf(m3 - # buf) + subarray(copy(buf3, 0, copy(buf1, 0, mkbuf(align↓(m2 + n3, EB_PAGE_SIZE)), 0, m2), m2, align↓(m2 + n3, EB_PAGE_SIZE) - m2), 0, n)) ]), is-aligned(m3, EB_PAGE_SIZE), is-aligned(n, EB_PAGE_SIZE), wbuf-cons(mkwbuf(buf1, m3, m2), mapped(buf), false), m3 + align↓(m2 + n3, EB_PAGE_SIZE) ≤ LEB_SIZE, # buf ≤ m3, n3 ≤ # buf3, m3 + m2 + n3 ≤ LEB_SIZE, EB_PAGE_SIZE ≤ m2 + n3, align↓(m2 + n3, EB_PAGE_SIZE) ≤ # buf3 + m2, m2 ≤ EB_PAGE_SIZE, m2 ≤ align↓(m2 + n3, EB_PAGE_SIZE), ⌊err0⌋ ⊦ n = 0, wbuf-cons (mkwbuf(buf1, m3, m2), mapped ( buf + mkempbuf(m3 - # buf) + subarray(copy(buf3, 0, copy(buf1, 0, mkbuf(align↓(m2 + n3, EB_PAGE_SIZE)), 0, m2), m2, align↓(m2 + n3, EB_PAGE_SIZE) - m2), 0, n)), true)

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)% ⊦ mapped(buf).data = buf; (s)% ⊦ mapped(buf).mapped?; (s)%n ≠ 0 ⊦ align↓(m, n) = 0 ↔ m < n; (s)% ⊦ mapped(buf) = mapped(buf0) ↔ buf = buf0; (s)%wbuf-cons-mapped: ⊦ wbuf-cons(wbuf, aleb, boolvar) → aleb.mapped?; (forward) from specification wbuf-base%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%aligndown-is-smaller: m ≠ 0 ⊦ n0 < align↓(n, m) → n0 < n; (forward) from specification align% ⊦ EB_PAGE_SIZE ≠ 0; (s)% ⊦ m < # avol → avol[m, aleb][m] = aleb; (s)% ⊦ mkwbuf(buf, m, m0).content = buf; (s)% ⊦ ⌊err⌋ → err ≠ ESUCCESS; (s)% ⊦ buffered(m).isbuf?; (s)% ⊦ aleb.mapped? ↔ (∃ buf. aleb = mapped(buf)); (as)% ⊦ m < n → m ≤ n; (s)% ⊦ m ≤ m; (s)% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)%n ≤ m ⊦ (m - n) + m0 ≤ n0 ↔ m + m0 ≤ n0 + n; (s)% ⊦ # mkbuf(n) = n; (s)% ⊦ # copy(buf, m, buf0, m0, n) = # buf0; (s)%n0 ≤ n ⊦ n - n0 ≤ m ↔ n ≤ m + n0; (s)% ⊦ m ≤ n → (n < m ↔ false); (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)%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)% ⊦ # avol[n, aleb] = # avol; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ buffered(m).leb = m; (s)