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Proof step 2 from proof inv-link (previous step)

c_inode.ino = old_dent.ino, old_dent.ino = dirs[ino].entries[old_dent.name], c_inode.nlink = files[old_dent.ino].nlink, p_inode.nlink = dirs[p_inode.ino].nlink, c_inode.nsubdirs = 0, p_inode.nsubdirs = dirs[p_inode.ino].nsubdirs, p_inode.size = dirs[p_inode.ino].size, old_dent.dentry?, p_inode.directory, new_dent.negdentry?, afs-cons(dirs, files), old_dent.ino ∈ files, p_inode.ino ∈ dirs, old_dent.name ∈ dirs[ino].entries, ino ∈ dirs, ¬ c_inode.directory, ¬ new_dent.name ∈ dirs[p_inode.ino].entries, links(old_dent.ino, dirs) ≠ ∅ ∨ old_dent.ino = ROOT_INO, links(p_inode.ino, dirs) ≠ ∅ ∨ p_inode.ino = ROOT_INO, links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO ⊦ ⟪afs_link#(old_dent; p_inode, c_inode, new_dent, err, dirs, files; asynced)⟫ afs-cons(dirs, files)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Rule argument

spec: dentry name: elim seq: ⊦ dent.dentry? → (str = dent.name ∧ m = dent.ino ↔ dent = mkdentry(str, m)) subst: [dent, str, m] → [old_dent, str, m]

Additional information

Used simplifier rules: ⊦ dent.dentry? → (str = dent.name ∧ m = dent.ino ↔ dent = mkdentry(str, m)); (elim) Used terms: old_dent, str, m