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Proof step 50 from proof refine-mkdir (previous step)

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, psynced → asynced ⊦ pre-mkdir(q + str ', md, ENOTDIR, user, root, abs-files(files), abs-of(of)) ∧ ⟨err0 := ENOTDIR; if err0 = ESUCCESS then root[q + str '] := dnode(md, ∅); psynced := ?⟩ (abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ ENOTDIR = err0), root[q].dir?, ino1 ∈ dirs

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 51:
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, ¬ root[q].dir?, ¬ ino1 ∈ dirs, psynced → asynced ⊦ ⟨err0 := ENOTDIR; if err0 = ESUCCESS then root[q + str '] := dnode(md, ∅); psynced := ?⟩ (abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ ENOTDIR = err0)

Rule argument

Additional information

Used simplifier rules: a: ⊦ (p + p0) + p1 = p + p0 + p1; from specification list[path]% ⊦ parent(p + str ') = p; (s)%⊦ pre-mkdir(p, md, ENOTDIR, user, root, fs, ofh) ↔ ¬ root[parent(p)].dir?; (s)