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Proof step 54 from proof refine-create (previous step)

fs = abs-files(files), path = q + str ', 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-parent(user, q, ROOT_INO, dirs, files), ROOT_INO ∈ dirs, ino1 ∈ files, ¬ root[q].dir?, ¬ ino1 ∈ dirs, psynced → asynced ⊦ ¬ root[parent(path)].dir? ∧ ⟨err0 := ENOTDIR; if err0 = ESUCCESS then choose fid with ¬ fid ∈ fs in {root[path] := fnode(fid); fs[fid] := mkfile(md, mkbuf(0))}; psynced := ?⟩ (fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ ENOTDIR = err0)

Heuristic dl case distinction applied rule case distinction

And obtained the following new goals

Proof step 55:
fs = abs-files(files), path = q + str ', 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-parent(user, q, ROOT_INO, dirs, files), ino1 ∈ files, ROOT_INO ∈ dirs, psynced → asynced ⊦ ⟨err0 := ENOTDIR; if err0 = ESUCCESS then choose fid with ¬ fid ∈ fs in {root[path] := fnode(fid); fs[fid] := mkfile(md, mkbuf(0))}; psynced := ?⟩ (fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ ENOTDIR = err0), root[q].dir?, ino1 ∈ dirs

Rule argument

pos: right 1

Additional information

Used simplifier rules: ⊦ parent(p + str ') = p; (s)%a: ⊦ (p + p0) + p1 = p + p0 + p1; from specification list[path]