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Proof step 138 from proof refine-rmdir (previous step)

isdir1 ↔ true, isdir2 ↔ true, entries[str] ∈ dirs ↔ root[q + str '].dir?, isdir ↔ p_inode.directory, isdir0 ↔ isdir, dirs[ino1] = mkdir(# entries, md, # links(ino1, dirs), m1, entries), err = ENOTEMPTY, err1 = err, err2 = ESUCCESS, err3 = ESUCCESS, fs = abs-files(files), ino = mkdentry(str, entries[str]).ino, inode = p_inode0, isdir, p_inode = getinode(ino, dirs, files), mkdentry(str, entries[str]).dentry?, 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), pre-iget(ino, dirs, files), pw(user, md), px(user, md), px-parent(user, q, ROOT_INO, dirs, files), str ∈ entries, ino1 ∈ dirs, psynced → asynced, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ ⟨posix_rmdir#(q + str ', user, fs, abs-of(of); err0, root; psynced)⟩ (fs = abs-files(files) ∧ abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ err1 = err0), p_inode.size = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 139:
⊦ ispath(p, ino, m, dirs, files) ∧ px-parent(user, p, ino, dirs, files) ∧ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) ∧ m ∈ dirs ∧ dirs[m] = mkdir(m0, md, n0, n1, entries) ∧ str ∈ entries ∧ entries[str] ∈ dirs → (dirs[entries[str]].entries = ∅ ↔ tree[p + str '].entries = ∅)
Proof step 140:
dirs[entries[str]].entries = ∅ ↔ root[q + str '].entries = ∅, dirs[ino1] = mkdir(# entries, md, # links(ino1, dirs), m1, entries), dirs[entries[str]].size ≠ 0, root.dir?, root[q].dir?, root[q + str '].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, entries[str] ∈ dirs, psynced → asynced, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ ⟨posix_rmdir#(q + str ', user, abs-files(files), abs-of(of); err0, root; psynced)⟩ (abs(root, ROOT_INO)(dirs) ∧ (psynced → asynced) ∧ ENOTEMPTY = err0)

Rule argument

Additional information

Used simplifier rules: dir-empty: ⊦ ispath(p, ino, m, dirs, files) ∧ px-parent(user, p, ino, dirs, files) ∧ abs(tree, ino)(dirs) ∧ fids-cons(tree, abs-files(files), ofh) ∧ afs-cons(dirs, files) ∧ m ∈ dirs ∧ dirs[m] = mkdir(m0, md, n0, n1, entries) ∧ str ∈ entries ∧ entries[str] ∈ dirs → (dirs[entries[str]].entries = ∅ ↔ tree[p + str '].entries = ∅);% ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (s)% ⊦ mkdentry(str, m).dentry?; (s)% ⊦ valid-ino(ino, dirs, files) ↔ ino ∈ dirs ∨ ino ∈ files; (s)% ⊦ pre-iget(ino, dirs, files) ↔ valid-ino(ino, dirs, files); (s)%⊦ getinode(ino, dirs, files) = (ino ∈ dirs ⊃ mkinode (ino, dirs[ino].meta, true, dirs[ino].nlink, dirs[ino].nsubdirs, dirs[ino].size) ;mkinode (ino, files[ino].meta, false, files[ino].nlink, 0, files[ino].size) ); (s)% ⊦ mkdentry(str, m).ino = m; (s)