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Proof step 27 from proof inv-unlink (previous step)

# links(entries0[str], dirs0) = c_inode.nlink, c_inode.ino = entries0[str], c_inode.nsubdirs = 0, files[entries0[str]] = mkfile(m0, md1, c_inode.nlink, content), dirs0[m] = mkdir(m2 + 1, md2, # links(m, dirs0), m3, entries0), dirs = dirs0[m, mkdir(m2, md2, # links(m, dirs0), m3, entries0 -- str)], ino = entries0[str], afs-cons(dirs0, files), m ∈ dirs0, str ∈ entries0, entries0[str] ∈ files, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪files[ino].nlink := files[ino].nlink - 1; dent := negdentry(mkdentry(str, entries0[str]).name); afs_inode_sync#(mkinode(m, md, true, # links(m, dirs0), m3, m2 + 1); dirs, files); afs_inode_sync#(c_inode; dirs, files); p_inode := (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ); c_inode := (c_inode.ino ∈ dirs ⊃ mkinode(c_inode.ino, dirs[c_inode.ino].meta, true, dirs[c_inode.ino].nlink, dirs[c_inode.ino].nsubdirs, dirs[c_inode.ino].size) ;mkinode(c_inode.ino, files[c_inode.ino].meta, false, files[c_inode.ino].nlink, 0, files[c_inode.ino].size) ); err := ESUCCESS; asynced := ?⟫ afs-cons(dirs, files), c_inode.directory

Heuristic symbolic execution applied rule assign right

And obtained the following new goals

Proof step 28:
# links(entries0[str], dirs0) = c_inode.nlink, c_inode.ino = entries0[str], c_inode.nsubdirs = 0, dirs0[m] = mkdir(m2 + 1, md2, # links(m, dirs0), m3, entries0), files0[entries0[str]] = mkfile(m0, md1, c_inode.nlink, content), dirs = dirs0[m, mkdir(m2, md2, # links(m, dirs0), m3, entries0 -- str)], files = files0[ino, files0[ino].nlink:= (files0[ino].nlink - 1)], ino = entries0[str], afs-cons(dirs0, files0), entries0[str] ∈ files0, str ∈ entries0, m ∈ dirs0, files0[ino].nlink ≥ 1, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪dent := negdentry(mkdentry(str, entries0[str]).name); afs_inode_sync#(mkinode(m, md, true, # links(m, dirs0), m3, m2 + 1); dirs, files); afs_inode_sync#(c_inode; dirs, files); p_inode := (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ); c_inode := (c_inode.ino ∈ dirs ⊃ mkinode(c_inode.ino, dirs[c_inode.ino].meta, true, dirs[c_inode.ino].nlink, dirs[c_inode.ino].nsubdirs, dirs[c_inode.ino].size) ;mkinode(c_inode.ino, files[c_inode.ino].meta, false, files[c_inode.ino].nlink, 0, files[c_inode.ino].size) ); err := ESUCCESS; asynced := ?⟫ afs-cons(dirs, files), c_inode.directory

Rule argument

Additional information

Used simplifier rules: ⊦ n ≥ m ↔ m ≤ n; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ m < 1 ↔ m = 0; (s)% ⊦ mkfile(m, md, m0, content).nlink = m0; (s)%size-zero-02: ⊦ # ls = 0 → ls = ∅; (forward) from specification set-basic[alink-set]%afs-cons-file-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n, content) → # links(ino, dirs) = n; (forward) from specification afs-base%⊦ p_ino ∈ dirs ∧ dirs[p_ino] = mkdir(m, md, n, n0, entries) ∧ str ∈ entries → links(entries[str], dirs) ≠ ∅; (s)