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Proof step 6 from proof inv-rmdir (previous step)

dirs[dirs[p_inode.ino].entries[str]].entries = ∅, p_inode.nlink = dirs[p_inode.ino].nlink, p_inode.nsubdirs = dirs[p_inode.ino].nsubdirs, p_inode.size = dirs[p_inode.ino].size, c_inode = mkinode (dirs[p_inode.ino].entries[str], md, true, dirs[dirs[p_inode.ino].entries[str]].nlink, dirs[dirs[p_inode.ino].entries[str]].nsubdirs, dirs[dirs[p_inode.ino].entries[str]].size), dent = mkdentry(str, dirs[p_inode.ino].entries[str]), dirs[p_inode.ino].entries[str] ≠ ROOT_INO, p_inode.directory, afs-cons(dirs, files), dirs[p_inode.ino].entries[str] ∈ 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)⟫ afs-cons(dirs, files)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 7:
dirs[dirs[m].entries[str]].entries = ∅, boolvar, c_inode = mkinode(dirs[m].entries[str], md, true, dirs[dirs[m].entries[str]].nlink, dirs[dirs[m].entries[str]].nsubdirs, dirs[dirs[m].entries[str]].size), dent = mkdentry(str, dirs[m].entries[str]), m0 = dirs[m].nlink, m1 = dirs[m].nsubdirs, m2 = dirs[m].size, p_inode = mkinode(m, md0, boolvar, m0, m1, m2), afs-cons(dirs, files), m ∈ dirs, str ∈ dirs[m].entries, dirs[m].entries[str] ∈ dirs, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪afs_rmdir#(; p_inode, c_inode, dent, err, dirs, files; asynced)⟫ afs-cons(dirs, files), dirs[m].entries[str] = 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, md0, 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, md0, boolvar, m0, m1, m2