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Proof step 281 from proof refine-truncate (previous step)

files[ino2] = mkfile(m0, md0, # links(ino2, dirs), content0), buf-opt = none, err = ESUCCESS, fs = abs-files(files), ino = 0, ino0 = ino, ino1 = ino4, ino4 = 0, inode = mkinode(ino2, md0, false, # links(ino2, dirs), 0, m0), pageno = m0 / VFS_PAGE_SIZE, root.dir?, dom of < ino3, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(path, ROOT_INO, ino2, dirs, files), of-cons(of, dirs, files), pw(user, md0), px-parent(user, path, ROOT_INO, dirs, files), ROOT_INO ∈ dirs, ino2 ∈ files, ⌊err0⌋ , psynced → asynced0 ⊦ [asynced := ?] ( of-cons(of, dirs, files) ∧ afs-cons(dirs, files) → ⟨posix_truncate#(path, n, user, root, abs-of(of); err1, fs; psynced)⟩ (fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err0 = err1)), VFS_PAGE_SIZE = 0, root[path].dir?, ino2 ∈ dirs

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 282:
⊦ ispath(p, ino, m, dirs, files) ∧ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) → p ∈ tree ∧ (tree[p].dir? ↔ m ∈ dirs)
Proof step 283:
⊦ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) → (p ∈ tree ↔ ispath(p, ino, dirs, files))
Proof step 284:
files[ino2] = mkfile(m0, md0, # links(ino2, dirs), content0), fs = abs-files(files), root.dir?, dom of < ino3, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(path, ROOT_INO, ino2, dirs, files), of-cons(of, dirs, files), pw(user, md0), px-parent(user, path, ROOT_INO, dirs, files), ROOT_INO ∈ dirs, ino2 ∈ files, ⌊err0⌋ , ¬ root[path].dir?, ¬ ino2 ∈ dirs, psynced → asynced0 ⊦ [asynced := ?] ⟨posix_truncate#(path, n, user, root, abs-of(of); err1, fs; psynced)⟩ (fs = abs-files(files) ∧ (psynced → asynced) ∧ err0 = err1)

Rule argument

Additional information

Used simplifier rules: path-in: ⊦ ispath(p, ino, m, dirs, files) ∧ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) → p ∈ tree ∧ (tree[p].dir? ↔ m ∈ dirs);%path-in-eq: ⊦ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) → (p ∈ tree ↔ ispath(p, ino, dirs, files));% ⊦ ispath(p, n, m, dirs, files) → ispath(p, n, dirs, files); (s)% ⊦ VFS_PAGE_SIZE ≠ 0; (s)