[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 149 from proof refine-truncate (previous step)

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 := ?⟩ ( 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 ∧ (psynced → asynced))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 150:
⊦ buf = buf0 ↔ # buf = # buf0 ∧ (∀ n. n < # buf → buf[n] = buf0[n])
Proof step 151:
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

Rule argument

spec: array, inst: buffer name: Extension seq: ⊦ buf = buf0 ↔ # buf = # buf0 ∧ (∀ n. n < # buf → buf[n] = buf0[n]) subst: [buf0, buf] → [( ( content0[m1, fill(content0[m1], zero, n1, n0)] upto (m1 * VFS_PAGE_SIZE + n1) ).stream to n ).buf, resize((content0.stream to m1 * VFS_PAGE_SIZE + n1).buf, n)] flags: <all paths>

Additional information

Used terms: ( ( content0[m1, fill(content0[m1], zero, n1, n0)] upto (m1 * VFS_PAGE_SIZE + n1) ).stream to n ).buf, resize((content0.stream to m1 * VFS_PAGE_SIZE + n1).buf, n)