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Proof step 142 from proof inv-rmdir (previous step)

dirs[entries0[str]] = mkdir(0, md1, # links(entries0[str], dirs), m1, ∅), dirs[ino1] = mkdir(m, md0, # links(ino1, dirs), m2, entries0), c_inode = p_inode0, dent = mkdentry(str, entries0[str]), err = ESUCCESS, ino = dent.ino, inode = mkinode(ino1, md0, true, # links(ino1, dirs), m2, m), p_ino = p_inode.ino, p_inode = inode, p_inode0 = mkinode(entries0[str], md1, true, # links(entries0[str], dirs), m1, 0), dent.dentry?, dom of < ino0, afs-cons(dirs, files), ispath(q, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), pre-rmdir(p_inode, c_inode, dent, dirs, files), pw(user, md0), px(user, md0), px-parent(user, q, ROOT_INO, dirs, files), str ∈ entries0, ino1 ∈ dirs, entries0[str] ∈ dirs, dirs[p_ino, dirs[p_ino].entries:= (dirs[p_ino].entries -- dent.name)][p_ino].size ≥ 1, dirs[p_ino, dirs[p_ino].entries:= (dirs[p_ino].entries -- dent.name)] [p_ino, dirs[p_ino, dirs[p_ino].entries:= (dirs[p_ino].entries -- dent.name)][p_ino] .size:= (dirs[p_ino, dirs[p_ino].entries:= (dirs[p_ino].entries -- dent.name)][p_ino].size - 1) ] [p_ino ] .nsubdirs ≥ 1, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ [dirs := dirs[p_ino, dirs[p_ino].entries:= (dirs[p_ino].entries -- dent.name)] [p_ino, dirs[p_ino, dirs[p_ino].entries:= (dirs[p_ino].entries -- dent.name)][p_ino] .size:= (dirs[p_ino, dirs[p_ino].entries:= (dirs[p_ino].entries -- dent.name)][p_ino].size - 1) ] [p_ino, dirs[p_ino, dirs[p_ino].entries:= (dirs[p_ino].entries -- dent.name)] [p_ino, dirs[p_ino, dirs[p_ino].entries:= (dirs[p_ino].entries -- dent.name)][p_ino] .size:= (dirs[p_ino, dirs[p_ino].entries:= (dirs[p_ino].entries -- dent.name)][p_ino].size - 1) ] [p_ino ] .nsubdirs:= ( dirs[p_ino, dirs[p_ino].entries:= (dirs[p_ino].entries -- dent.name)] [p_ino, dirs[p_ino, dirs[p_ino].entries:= (dirs[p_ino].entries -- dent.name)][p_ino] .size:= (dirs[p_ino, dirs[p_ino].entries:= (dirs[p_ino].entries -- dent.name)][p_ino].size - 1) ] [p_ino ] .nsubdirs - 1) ]; afs_drop_nlink#(ino; dirs, files); dent := negdentry(dent.name); afs_inode_sync#(p_inode; dirs, files); afs_inode_sync#(c_inode; dirs, files); p_inode := getinode(p_inode.ino, dirs, files); c_inode := getinode(c_inode.ino, dirs, files); err := ESUCCESS; asynced := ?] (afs-cons(dirs, files) → ⟪vfs_put_inode#(c_inode, of, asynced; err, dirs, files)⟫ (of-cons(of, dirs, files) ∧ afs-cons(dirs, files))), entries0[str] = ROOT_INO

Heuristic symbolic execution applied rule assign right

And obtained the following new goals

Proof step 143:
dirs0[ino1] = mkdir(m, md0, # links(ino1, dirs0), m2, entries0), dirs0[entries0[str]] = mkdir(0, md1, # links(entries0[str], dirs0), m1, ∅), c_inode = p_inode0, dent = mkdentry(str, entries0[str]), dirs = dirs0[p_ino, dirs0[p_ino].entries:= (dirs0[p_ino].entries -- dent.name)] [p_ino, dirs0[p_ino, dirs0[p_ino].entries:= (dirs0[p_ino].entries -- dent.name)][p_ino] .size:= (dirs0[p_ino, dirs0[p_ino].entries:= (dirs0[p_ino].entries -- dent.name)][p_ino].size - 1) ] [p_ino, dirs0[p_ino, dirs0[p_ino].entries:= (dirs0[p_ino].entries -- dent.name)] [p_ino, dirs0[p_ino, dirs0[p_ino].entries:= (dirs0[p_ino].entries -- dent.name)][p_ino] .size:= (dirs0[p_ino, dirs0[p_ino].entries:= (dirs0[p_ino].entries -- dent.name)][p_ino].size - 1) ] [p_ino ] .nsubdirs:= ( dirs0[p_ino, dirs0[p_ino].entries:= (dirs0[p_ino].entries -- dent.name)] [p_ino, dirs0[p_ino, dirs0[p_ino].entries:= (dirs0[p_ino].entries -- dent.name)][p_ino] .size:= (dirs0[p_ino, dirs0[p_ino].entries:= (dirs0[p_ino].entries -- dent.name)][p_ino].size - 1) ] [p_ino ] .nsubdirs - 1) ], err = ESUCCESS, ino = dent.ino, inode = mkinode(ino1, md0, true, # links(ino1, dirs0), m2, m), p_ino = p_inode.ino, p_inode = inode, p_inode0 = mkinode(entries0[str], md1, true, # links(entries0[str], dirs0), m1, 0), dent.dentry?, dom of < ino0, afs-cons(dirs0, files), ispath(q, ROOT_INO, ino1, dirs0, files), of-cons(of, dirs0, files), pre-rmdir(p_inode, c_inode, dent, dirs0, files), pw(user, md0), px(user, md0), px-parent(user, q, ROOT_INO, dirs0, files), entries0[str] ∈ dirs0, ino1 ∈ dirs0, str ∈ entries0, dirs0[p_ino, dirs0[p_ino].entries:= (dirs0[p_ino].entries -- dent.name)] [p_ino, dirs0[p_ino, dirs0[p_ino].entries:= (dirs0[p_ino].entries -- dent.name)][p_ino] .size:= (dirs0[p_ino, dirs0[p_ino].entries:= (dirs0[p_ino].entries -- dent.name)][p_ino].size - 1) ] [p_ino ] .nsubdirs ≥ 1, dirs0[p_ino, dirs0[p_ino].entries:= (dirs0[p_ino].entries -- dent.name)][p_ino].size ≥ 1, links(ino1, dirs0) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ [afs_drop_nlink#(ino; dirs, files); dent := negdentry(dent.name); afs_inode_sync#(p_inode; dirs, files); afs_inode_sync#(c_inode; dirs, files); p_inode := getinode(p_inode.ino, dirs, files); c_inode := getinode(c_inode.ino, dirs, files); err := ESUCCESS; asynced := ?] (afs-cons(dirs, files) → ⟪vfs_put_inode#(c_inode, of, asynced; err, dirs, files)⟫ (of-cons(of, dirs, files) ∧ afs-cons(dirs, files))), entries0[str] = ROOT_INO

Proof step 142 from proof inv-rmdir (previous step)

Heuristic symbolic execution applied rule assign right

And obtained the following new goals

Rule argument

Additional information