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Proof step 151 from proof refine-truncate (previous step)

VFS_PAGE_SIZE = n0 + n1, files1[ino2] = mkfile(m1 * VFS_PAGE_SIZE + n1, md0, # links(ino2, dirs), content0), root.dir?, n1 < VFS_PAGE_SIZE, dom of < ino3, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files1[ino2, mkfile(n, md0, # links(ino2, dirs), content0[m1, fill(content0[m1], zero, n1, n0)] upto (m1 * VFS_PAGE_SIZE + n1))]), afs-cons(dirs, files1), fids-cons(root, abs-files(files1), abs-of(of)), ispath(path, ROOT_INO, ino2, dirs, files1), of-cons (of, dirs, files1[ino2, mkfile(n, md0, # links(ino2, dirs), content0[m1, fill(content0[m1], zero, n1, n0)] upto (m1 * VFS_PAGE_SIZE + n1))]), of-cons(of, dirs, files1), pw(user, md0), px-parent(user, path, ROOT_INO, dirs, files1), ROOT_INO ∈ dirs, ino2 ∈ files1, m1 ∈ content0, m1 * VFS_PAGE_SIZE + n1 ≤ n, psynced → asynced0 ⊦ ⟨psynced := ?⟩ ( ( # resize((content0.stream to m1 * VFS_PAGE_SIZE + n1).buf, n) = # ((content0[m1, fill(content0[m1], zero, n1, n0)] upto (m1 * VFS_PAGE_SIZE + n1)).stream to n).buf ∧ (∀ n2. n2 < # resize((content0.stream to m1 * VFS_PAGE_SIZE + n1).buf, n) → resize((content0.stream to m1 * VFS_PAGE_SIZE + n1).buf, n)[n2] = ((content0[m1, fill(content0[m1], zero, n1, n0)] upto (m1 * VFS_PAGE_SIZE + n1)).stream to n).buf[n2])) ∧ (psynced → asynced)), n0 = 0, n1 = 0, root[path].dir?, ino2 ∈ dirs

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 152:
VFS_PAGE_SIZE = n0 + n1, files1[ino2] = mkfile(m1 * VFS_PAGE_SIZE + n1, md0, # links(ino2, dirs), content0), n0 ≠ 0, n1 ≠ 0, root.dir?, dom of < ino3, n1 < VFS_PAGE_SIZE, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files1), afs-cons(dirs, files1[ino2, mkfile(n, md0, # links(ino2, dirs), content0[m1, fill(content0[m1], zero, n1, n0)] upto (m1 * VFS_PAGE_SIZE + n1))]), fids-cons(root, abs-files(files1), abs-of(of)), ispath(path, ROOT_INO, ino2, dirs, files1), of-cons(of, dirs, files1), of-cons (of, dirs, files1[ino2, mkfile(n, md0, # links(ino2, dirs), content0[m1, fill(content0[m1], zero, n1, n0)] upto (m1 * VFS_PAGE_SIZE + n1))]), pw(user, md0), px-parent(user, path, ROOT_INO, dirs, files1), m1 ∈ content0, ino2 ∈ files1, ROOT_INO ∈ dirs, m1 * VFS_PAGE_SIZE + n1 ≤ n, ¬ root[path].dir?, ¬ ino2 ∈ dirs, psynced → asynced0 ⊦ ⟨psynced := ?⟩ ( (∀ n2. n2 < n → (m1 * VFS_PAGE_SIZE + n1 ≤ n2 ⊃ zero;getbyte(n2, content0)) = getbyte(n2, content0[m1, fill(content0[m1], zero, n1, n0)] upto (m1 * VFS_PAGE_SIZE + n1))) ∧ (psynced → asynced))

Rule argument

Additional information

Used simplifier rules: ⊦ ⌜m⌝ < ⌜n⌝ ↔ m < n; (s)% ⊦ content.stream[n] = getbyte(n, content); (s)%m < n, ¬ # σ0 < ⌜n⌝ ⊦ (σ0 to n)[m] = σ0[m]; (s)%finp(σ), ⌜n⌝ < # σ ⊦ σ.buf[n] = σ[n]; (s)% ⊦ m ≤ n → (n < m ↔ false); (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ ⌜n⌝ < ⌜m⌝ + ⌜n0⌝ ↔ n < m + n0; (s)%add-comm: ⊦ n∞1 + n∞2 = n∞2 + n∞1; from specification nat-inf%add-assoc: ⊦ (n∞ + n∞1) + n∞2 = n∞ + n∞1 + n∞2; from specification nat-inf%n∞ ≠ ∞ ⊦ (⌜m⌝ + n∞).n = m + n∞.n; (s)% ⊦ ⌜m⌝ ≠ ∞; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ ⌜m + n⌝ = ⌜m⌝ + ⌜n⌝ ; (s)% ⊦ m < n → resize(buf, n)[m] = (# buf ≤ m ∧ m < n ⊃ zero;buf[m]); (s)% ⊦ ⌜m⌝ .n = m; (s)%¬ # σ0 < ⌜n⌝ ⊦ #(σ0 to n) = ⌜n⌝ ; (s)% ⊦ ¬ ∞ < n∞; (s)% ⊦ # content.stream = ∞; (s)%finp(σ) ⊦ # σ.buf = (# σ).n; (s)% ⊦ finp(σ0 to m); (s)% ⊦ # resize(buf, n) = n; (s)