[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 134 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), dent = mkdentry(str, entries0[str]), err = ESUCCESS, inode = mkinode(ino1, md0, true, # links(ino1, dirs), m2, m), p_inode = mkinode(entries0[str], md1, true, # links(entries0[str], dirs), m1, 0), entries0[str] ≠ ROOT_INO, dom of < ino0, afs-cons(dirs, files), ispath(q, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), pw(user, md0), px(user, md0), px-parent(user, q, ROOT_INO, dirs, files), str ∈ entries0, ino1 ∈ dirs, entries0[str] ∈ dirs, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ [afs_rmdir#(; inode, p_inode, dent, err, dirs, files; asynced)] (afs-cons(dirs, files) → ⟪vfs_put_inode#(p_inode, of, asynced; err, dirs, files)⟫ (of-cons(of, dirs, files) ∧ afs-cons(dirs, files)))

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 135:
dirs[ino1] = mkdir(m, md0, # links(ino1, dirs), m2, entries0), dirs[entries0[str]] = mkdir(0, md1, # links(entries0[str], dirs), m1, ∅), c_inode = p_inode0, dent = mkdentry(str, entries0[str]), err = ESUCCESS, inode = mkinode(ino1, md0, true, # links(ino1, dirs), m2, m), p_inode = inode, p_inode0 = mkinode(entries0[str], md1, true, # links(entries0[str], dirs), m1, 0), dom of < ino0, afs-cons(dirs, files), ispath(q, ROOT_INO, ino1, dirs, files), of-cons(of, dirs, files), pw(user, md0), px(user, md0), px-parent(user, q, ROOT_INO, dirs, files), entries0[str] ∈ dirs, ino1 ∈ dirs, str ∈ entries0, links(ino1, dirs) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ [if pre-rmdir(p_inode, c_inode, dent, dirs, files) then { let p_ino = p_inode.ino in {dirs[p_ino].entries := dirs[p_ino].entries -- dent.name; dirs[p_ino].size := dirs[p_ino].size - 1; dirs[p_ino].nsubdirs := dirs[p_ino].nsubdirs - 1; let ino = dent.ino in 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} or fail#(; ; err); asynced := ?} else abort] (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

Rule argument

pos: right 1

Additional information

Used simplifier rules: afs_rmdir#(; P_INODE, C_INODE, DENT, ERR, DIRS, FILES; ASYNCED) {if pre-rmdir(P_INODE, C_INODE, DENT, DIRS, FILES) then { let P_INO = P_INODE.ino in {DIRS[P_INO].entries := DIRS[P_INO].entries -- DENT.name; DIRS[P_INO].size := DIRS[P_INO].size - 1; DIRS[P_INO].nsubdirs := DIRS[P_INO].nsubdirs - 1; let INO = DENT.ino in 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} or fail#(; ; ERR); ASYNCED := ?} else abort };