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Proof step 9 from proof afs-cons-rename-dir-dentry (previous step)

dirs[dirs[new_parent_inode.ino].entries[str]].entries = ∅, old_child_inode.ino = dirs[old_parent_inode.ino].entries[str0], old_child_inode.nlink = dirs[old_child_inode.ino].nlink, new_parent_inode.nlink = dirs[new_parent_inode.ino].nlink, old_parent_inode.nlink = dirs[old_parent_inode.ino].nlink, old_child_inode.nsubdirs = dirs[old_child_inode.ino].nsubdirs, new_parent_inode.nsubdirs = dirs[new_parent_inode.ino].nsubdirs, old_parent_inode.nsubdirs = dirs[old_parent_inode.ino].nsubdirs, old_child_inode.size = dirs[old_child_inode.ino].size, new_parent_inode.size = dirs[new_parent_inode.ino].size, old_parent_inode.size = dirs[old_parent_inode.ino].size, new_child_inode = mkinode (dirs[new_parent_inode.ino].entries[str], md, true, dirs[dirs[new_parent_inode.ino].entries[str]].nlink, dirs[dirs[new_parent_inode.ino].entries[str]].nsubdirs, dirs[dirs[new_parent_inode.ino].entries[str]].size), new_dent = mkdentry(str, dirs[new_parent_inode.ino].entries[str]), old_dent = mkdentry(str0, old_child_inode.ino), dirs[new_parent_inode.ino].entries[str] ≠ ROOT_INO, old_child_inode.directory, new_parent_inode.directory, old_parent_inode.directory, afs-cons(dirs, files), str ∈ dirs[new_parent_inode.ino].entries, str0 ∈ dirs[old_parent_inode.ino].entries, dirs[new_parent_inode.ino].entries[str] ∈ dirs, old_child_inode.ino ∈ dirs, new_parent_inode.ino ∈ dirs, old_parent_inode.ino ∈ dirs, new_parent_inode.ino = old_parent_inode.ino → new_parent_inode.meta = old_parent_inode.meta, links(new_parent_inode.ino, dirs) ≠ ∅ ∨ new_parent_inode.ino = ROOT_INO, links(old_parent_inode.ino, dirs) ≠ ∅ ∨ old_parent_inode.ino = 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)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 10:
dirs[dirs[new_parent_inode.ino].entries[str]].entries = ∅, old_parent_inode.nlink = dirs[old_parent_inode.ino].nlink, new_parent_inode.nlink = dirs[new_parent_inode.ino].nlink, old_parent_inode.nsubdirs = dirs[old_parent_inode.ino].nsubdirs, new_parent_inode.nsubdirs = dirs[new_parent_inode.ino].nsubdirs, old_parent_inode.size = dirs[old_parent_inode.ino].size, new_parent_inode.size = dirs[new_parent_inode.ino].size, boolvar, m = dirs[old_parent_inode.ino].entries[str0], m0 = dirs[m].nlink, m1 = dirs[m].nsubdirs, m2 = dirs[m].size, new_child_inode = mkinode (dirs[new_parent_inode.ino].entries[str], md, true, dirs[dirs[new_parent_inode.ino].entries[str]].nlink, dirs[dirs[new_parent_inode.ino].entries[str]].nsubdirs, dirs[dirs[new_parent_inode.ino].entries[str]].size), new_dent = mkdentry(str, dirs[new_parent_inode.ino].entries[str]), old_child_inode = mkinode(m, md0, boolvar, m0, m1, m2), old_dent = mkdentry(str0, m), old_parent_inode.directory, new_parent_inode.directory, afs-cons(dirs, files), old_parent_inode.ino ∈ dirs, new_parent_inode.ino ∈ dirs, m ∈ dirs, dirs[new_parent_inode.ino].entries[str] ∈ dirs, str0 ∈ dirs[old_parent_inode.ino].entries, str ∈ dirs[new_parent_inode.ino].entries, new_parent_inode.ino = old_parent_inode.ino → new_parent_inode.meta = old_parent_inode.meta, links(old_parent_inode.ino, dirs) ≠ ∅ ∨ old_parent_inode.ino = ROOT_INO, links(new_parent_inode.ino, dirs) ≠ ∅ ∨ new_parent_inode.ino = 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), dirs[new_parent_inode.ino].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] → [old_child_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: old_child_inode, m, md0, boolvar, m0, m1, m2