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Proof step 574 from proof refine-rmdir (previous step)

# links(entries0[str], dirs) = m0, 0 = m, root[q + str '] = dnode(md1, ∅), dirs[ino1] = mkdir(# entries0, md2, # links(ino1, dirs), m1, entries0), dirs[entries0[str]] = mkdir(0, md0, m0, m2, ∅), dirs[entries0[str]] = mkdir(m, md, m0, m2, entries), 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, md2), px(user, md2), px-parent(user, q, ROOT_INO, dirs, files), entries0[str] ∈ dirs, ino1 ∈ dirs, str ∈ entries0, psynced → asynced0, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ [fail#(; ; err); asynced := ?; files0 := files; vfs_put_inode#(mkinode(entries0[str], md0, true, m0, m2, 0), of, asynced; err, dirs, files)] ( of-cons(of, dirs, files) ∧ afs-cons(dirs, files) → ⟨posix_rmdir#(q + str ', user, abs-files(files0), abs-of(of); err1, root; psynced)⟩ (abs-files(files0) = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err = err1))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 575:
dirs[entries0[str]] = mkdir(0, md, # links(entries0[str], dirs), m2, ∅), dirs[ino1] = mkdir(# entries0, md2, # links(ino1, dirs), m1, entries0), root[q + str '] = dnode(md1, ∅), 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, md2), px(user, md2), px-parent(user, q, ROOT_INO, dirs, files), str ∈ entries0, ino1 ∈ dirs, entries0[str] ∈ dirs, psynced → asynced0, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ [fail#(; ; err); asynced := ?; files0 := files; vfs_put_inode#(mkinode(entries0[str], md, true, # links(entries0[str], dirs), m2, 0), of, asynced; err, dirs, files)] ( of-cons(of, dirs, files) ∧ afs-cons(dirs, files) → ⟨posix_rmdir#(q + str ', user, abs-files(files0), abs-of(of); err1, root; psynced)⟩ (abs-files(files0) = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err = err1))

Rule argument

Additional information

Used simplifier rules: ⊦ mkdir(m, md, m0, m1, entries) = mkdir(m2, md0, m3, m4, entries0) ↔ m = m2 ∧ md = md0 ∧ m0 = m3 ∧ m1 = m4 ∧ entries = entries0; (ws)