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Proof step 5 from proof crash-neutral-rmdir (previous step)

dirs[c_inode.ino].entries = ∅, c_inode.ino = dirs[p_inode.ino].entries[str], c_inode.nlink = dirs[c_inode.ino].nlink, p_inode.nlink = dirs[p_inode.ino].nlink, c_inode.nsubdirs = dirs[c_inode.ino].nsubdirs, p_inode.nsubdirs = dirs[p_inode.ino].nsubdirs, c_inode.size = dirs[c_inode.ino].size, p_inode.size = dirs[p_inode.ino].size, dent = mkdentry(str, c_inode.ino), dirs0 = dirs \ orphans(dirs, files), files0 = files \ orphans(dirs, files), c_inode.ino ≠ ROOT_INO, c_inode.directory, p_inode.directory, afs-cons(dirs, files), c_inode.ino ∈ dirs, str ∈ dirs[p_inode.ino].entries, p_inode.ino ∈ dirs, links(p_inode.ino, dirs) ≠ ∅ ∨ p_inode.ino = ROOT_INO ⊦ ⟨afs_rmdir#(; p_inode, c_inode, dent, err, dirs, files; asynced)⟩ (asynced ∧ dirs0 = dirs \ orphans(dirs, files) ∧ files0 = files \ orphans(dirs, files))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 6:
dirs[c_inode.ino].entries = ∅, c_inode.ino = dirs[m].entries[str], c_inode.nlink = dirs[c_inode.ino].nlink, c_inode.nsubdirs = dirs[c_inode.ino].nsubdirs, c_inode.size = dirs[c_inode.ino].size, boolvar, dent = mkdentry(str, c_inode.ino), dirs0 = dirs \ orphans(dirs, files), files0 = files \ orphans(dirs, files), m0 = dirs[m].nlink, m1 = dirs[m].nsubdirs, m2 = dirs[m].size, p_inode = mkinode(m, md, boolvar, m0, m1, m2), c_inode.directory, afs-cons(dirs, files), m ∈ dirs, str ∈ dirs[m].entries, c_inode.ino ∈ dirs, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟨afs_rmdir#(; p_inode, c_inode, dent, err, dirs, files; asynced)⟩ (asynced ∧ dirs0 = dirs \ orphans(dirs, files) ∧ files0 = files \ orphans(dirs, files)), c_inode.ino = ROOT_INO

Rule argument

spec: inode name: elim seq: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2) subst: [inode, m, md, boolvar, m0, m1, m2] → [p_inode, m, md, boolvar, m0, m1, m2]

Additional information

Used simplifier rules: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2); (elim) Used terms: p_inode, m, md, boolvar, m0, m1, m2