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Proof step 99 from proof refine-fsync (previous step)

files[ino1] = mkfile(m0, md0, # links(ino1, dirs), content0), root.dir?, dom of < ino0, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(path, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), pr(user, md0), px-parent(user, path, ROOT_INO, dirs, files), ino1 ∈ files, ROOT_INO ∈ dirs, psynced → asynced0 ⊦ root[path].dir?, pre-fsync(path, isdir, ESUCCESS, user, root, abs-files(files), abs-of(of)), ino1 ∈ dirs

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: posix-pre name: pre-fsync-esuccess seq: ⊦ pre-fsync(p, datasyncp, ESUCCESS, user, root, fs, ofh) ↔ p ∈ root ∧ ¬ root[p].dir? ∧ pr(user, p, root, fs) subst: [ofh, fs, root, user, datasyncp, p] → [abs-of(of), abs-files(files), root, user, isdir, path] flags: <all paths>

Additional information

Used simplifier rules: 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));%pr: ⊦ 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) → ( pr(user, p, tree, abs-files(files)) ↔ pr(user, meta(ε, m, dirs, files)));% ⊦ ispath(p, n, m, dirs, files) → ispath(p, n, dirs, files); (s)%¬ ino ∈ dirs ⊦ ino ∈ files → meta(ε, ino, dirs, files) = files[ino].meta; (s)% ⊦ mkfile(m, md, m0, content).meta = md; (s) Used terms: abs-of(of), abs-files(files), root, user, isdir, path