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Proof step 18 from proof afs-cons-rename-dir-negdentry (previous step)

dirs[entries1[str]] = mkdir(m2, md3, # links(entries1[str], dirs), m5, entries0), dirs[m0] = mkdir(m1, md2, # links(m0, dirs), m3, entries), dirs[m] = mkdir(m4, md4, m6, m7, entries1), new_dent = negdentry(str0), new_parent_inode = mkinode(m0, md1, true, # links(m0, dirs), m3, m1), old_child_inode = mkinode(entries1[str], md, true, # links(entries1[str], dirs), m5, m2), old_dent = mkdentry(str, entries1[str]), old_parent_inode = mkinode(m, md0, true, m6, m7, m4), afs-cons(dirs, files), m0 ∈ dirs, m ∈ dirs, entries1[str] ∈ dirs, str ∈ entries1, m0 = m → md1 = md0, links(m0, dirs) ≠ ∅ ∨ m0 = ROOT_INO, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪afs_rename#(; old_parent_inode, new_parent_inode, old_child_inode, new_child_inode, old_dent, new_dent, err, dirs, files; asynced)⟫ afs-cons(dirs, files), str0 ∈ entries

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 19:
dirs[entries1[str]] = mkdir(m2, md3, # links(entries1[str], dirs), m5, entries0), dirs[m0] = mkdir(m1, md2, # links(m0, dirs), m3, entries), dirs[m] = mkdir(m4, md4, # links(m, dirs), m7, entries1), new_dent = negdentry(str0), new_parent_inode = mkinode(m0, md1, true, # links(m0, dirs), m3, m1), old_child_inode = mkinode(entries1[str], md, true, # links(entries1[str], dirs), m5, m2), old_dent = mkdentry(str, entries1[str]), old_parent_inode = mkinode(m, md0, true, # links(m, dirs), m7, m4), afs-cons(dirs, files), m0 ∈ dirs, m ∈ dirs, entries1[str] ∈ dirs, str ∈ entries1, ¬ str0 ∈ entries, m0 = m → md1 = md0, links(m0, dirs) ≠ ∅ ∨ m0 = ROOT_INO, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪afs_rename#(; old_parent_inode, new_parent_inode, old_child_inode, new_child_inode, old_dent, new_dent, err, dirs, files; asynced)⟫ afs-cons(dirs, files)

Rule argument

Additional information

Used simplifier rules: afs-cons-dir-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs ∧ dirs[ino] = mkdir(n0, md, n, n1, entries) → # links(ino, dirs) = n; (forward) from specification afs-base