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Proof step 570 from proof refine-link (previous step)

dirs[ino1] = mkdir(# entries, md, # links(ino1, dirs), m1, entries), root.dir?, root[q].dir?, dom of < ino0, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(q, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), px(user, md), px-parent(user, q, ROOT_INO, dirs, files), ino1 ∈ dirs, psynced → asynced, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ pre-link(q + str ', path', ENOENT, user, root, abs-files(files), abs-of(of)) ∧ ⟨err0 := ENOENT; if err0 = ESUCCESS then let fid = root[q + str '].fid in root[path'] := fnode(fid); psynced := ?⟩ (abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ ENOENT = err0), path' = ε, str ∈ entries

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 571:
⊦ pre-link(p, p', ENOENT, user, root, fs, ofh) ↔ ¬ p ∈ root ∨ ¬ parent(p') ∈ root
Proof step 572:
dirs[ino1] = mkdir(# entries, md, # links(ino1, dirs), m1, entries), root[q].dir?, root.dir?, dom of < ino0, abs(root, ROOT_INO)(dirs), afs-cons(dirs, files), fids-cons(root, abs-files(files), abs-of(of)), ispath(q, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), px(user, md), px-parent(user, q, ROOT_INO, dirs, files), ino1 ∈ dirs, psynced → asynced, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ (¬ q + str ' ∈ root ∨ ¬ parent(path') ∈ root) ∧ ⟨err0 := ENOENT; if err0 = ESUCCESS then let fid = root[q + str '].fid in root[path'] := fnode(fid); psynced := ?⟩ (abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ ENOENT = err0), path' = ε, str ∈ entries

Rule argument

spec: posix-pre name: pre-link-enoent seq: ⊦ pre-link(p, p', ENOENT, user, root, fs, ofh) ↔ ¬ p ∈ root ∨ ¬ parent(p') ∈ root subst: [ofh, fs, root, user, p', p] → [abs-of(of), abs-files(files), root, user, path', q + str '] flags: <all paths>

Additional information

Used terms: abs-of(of), abs-files(files), root, user, path', q + str '