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Proof step 145 from proof refine-truncate (previous step)

VFS_PAGE_SIZE = n0 + m0 % VFS_PAGE_SIZE, files1[ino2] = mkfile(m0, md0, # links(ino2, dirs), content0), root[path] = fnode(fid), root.dir?, dom of < ino3, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files1), afs-cons (dirs, files1 [ino2, mkfile(n, md0, # links(ino2, dirs), content0[m0 / VFS_PAGE_SIZE, fill(content0[m0 / VFS_PAGE_SIZE], zero, m0 % VFS_PAGE_SIZE, n0)] upto m0) ]), 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[m0 / VFS_PAGE_SIZE, fill(content0[m0 / VFS_PAGE_SIZE], zero, m0 % VFS_PAGE_SIZE, n0)] upto m0) ]), pw(user, md0), px-parent(user, path, ROOT_INO, dirs, files1), m0 / VFS_PAGE_SIZE ∈ content0, ino2 ∈ files1, ROOT_INO ∈ dirs, fid ∈ abs-files(files1), m0 ≤ n, psynced → asynced0 ⊦ ⟨psynced := ?⟩ ( abs-files(files1)[fid, mkfile(abs-files(files1)[fid].meta, resize(abs-files(files1)[fid].content, n))] = abs-files (files1 [ino2, mkfile (n, md0, # links(ino2, dirs), content0[m0 / VFS_PAGE_SIZE, fill(content0[m0 / VFS_PAGE_SIZE], zero, m0 % VFS_PAGE_SIZE, n0)] upto m0) ]) ∧ (psynced → asynced)), m0 % VFS_PAGE_SIZE = 0, root[path].dir?, ino2 ∈ dirs

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 146:
⊦ ispath(p, ino, m, dirs, files) ∧ px-parent(user, p, ino, dirs, files) ∧ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) ∧ m ∈ files → (tree[p] = fnode(fid) ↔ fid = ⌜m⌝ )
Proof step 147:
VFS_PAGE_SIZE = n0 + m0 % VFS_PAGE_SIZE, files1[ino2] = mkfile(m0, md0, # links(ino2, dirs), content0), m0 % VFS_PAGE_SIZE ≠ 0, root.dir?, dom of < ino3, abs(root, ROOT_INO)(dirs), afs-cons (dirs, files1 [ino2, mkfile(n, md0, # links(ino2, dirs), content0[m0 / VFS_PAGE_SIZE, fill(content0[m0 / VFS_PAGE_SIZE], zero, m0 % VFS_PAGE_SIZE, n0)] upto m0) ]), 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[m0 / VFS_PAGE_SIZE, fill(content0[m0 / VFS_PAGE_SIZE], zero, m0 % VFS_PAGE_SIZE, n0)] upto m0) ]), of-cons(of, dirs, files1), pw(user, md0), px-parent(user, path, ROOT_INO, dirs, files1), ROOT_INO ∈ dirs, ino2 ∈ files1, m0 / VFS_PAGE_SIZE ∈ content0, m0 ≤ n, ¬ root[path].dir?, ¬ ino2 ∈ dirs, psynced → asynced0 ⊦ ⟨psynced := ?⟩ ( resize((content0.stream to m0).buf, n) = ((content0[m0 / VFS_PAGE_SIZE, fill(content0[m0 / VFS_PAGE_SIZE], zero, m0 % VFS_PAGE_SIZE, n0)] upto m0).stream to n).buf ∧ (psynced → asynced))

Rule argument

Additional information

Used simplifier rules: fid-ino: ⊦ ispath(p, ino, m, dirs, files) ∧ px-parent(user, p, ino, dirs, files) ∧ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) ∧ m ∈ files → (tree[p] = fnode(fid) ↔ fid = ⌜m⌝ );% ⊦ mkfile(m, md, m0, content).size = m; (s)% ⊦ mkfile(m, md, m0, content).content = content; (s)% ⊦ mkfile(m, md, m0, content).meta = md; (s)%⊦ ino ∈ files → ( abs-files(files)[⌜ino⌝ , f] = abs-files(files[ino, af]) ↔ f.meta = af.meta ∧ f.content = (af.content.stream to af.size).buf); (s)% ⊦ mkfile(md, buf).content = buf; (s)% ⊦ mkfile(md, buf).meta = md; (s)%⊦ ino ∈ files → abs-files(files)[⌜ino⌝ ] = mkfile (files[ino].meta, (files[ino].content.stream to files[ino].size).buf); (s)% ⊦ ⌜ino⌝ ∈ abs-files(files) ↔ ino ∈ files; (s)