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Proof step 659 from proof refine-rmdir (previous step)

entries[str] ∈ dirs ↔ root[q + str '].dir?, 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), pw(user, md), px(user, md), px-parent(user, q, ROOT_INO, dirs, files), ino1 ∈ dirs, str ∈ entries, ⌊err1⌋ , psynced → asynced, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO, entries[str] ∈ dirs ∨ entries[str] ∈ files ⊦ pre-rmdir(q + str ', err1, user, root, abs-files(files), abs-of(of)) ∧ ⟨err0 := err1; if err0 = ESUCCESS then root := root -- (q + str '); psynced := ?⟩ (abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err1 = err0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 660:
entries[str] ∈ dirs ↔ root[q + str '].dir?, 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), pw(user, md), px(user, md), px-parent(user, q, ROOT_INO, dirs, files), str ∈ entries, ino1 ∈ dirs, ⌊err1⌋ , psynced → asynced, entries[str] ∈ dirs ∨ entries[str] ∈ files, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ ⟨err0 := err1; if err0 = ESUCCESS then root := root -- (q + str '); psynced := ?⟩ (abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err1 = err0)

Rule argument

Additional information

Used simplifier rules: ⊦ ⌊err⌋ → pre-rmdir(p, err, user, root, fs, ofh); (s)