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Proof step 3 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), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), 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, asynced → synced(files, icache, pcache), 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 ⊦ ⟪cache_link#(old_dent; p_inode, c_inode, new_dent, err, dirs, files, icache, dcache, asynced0)⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced → synced(files, icache, pcache)) ∧ afs-cons(dirs, files))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 4:
c_inode.ino = m, p_inode.nlink = dirs[p_inode.ino].nlink, c_inode.nlink = files[m].nlink, p_inode.nsubdirs = dirs[p_inode.ino].nsubdirs, c_inode.nsubdirs = 0, p_inode.size = dirs[p_inode.ino].size, m = dirs[ino].entries[str], old_dent = mkdentry(str, m), old_dent.dentry?, p_inode.directory, new_dent.negdentry?, afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), ino ∈ dirs, str ∈ dirs[ino].entries, p_inode.ino ∈ dirs, m ∈ files, asynced → synced(files, icache, pcache), links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO, links(p_inode.ino, dirs) ≠ ∅ ∨ p_inode.ino = ROOT_INO, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪cache_link#(old_dent; p_inode, c_inode, new_dent, err, dirs, files, icache, dcache, asynced0)⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced → synced(files, icache, pcache)) ∧ afs-cons(dirs, files)), c_inode.directory, new_dent.name ∈ dirs[p_inode.ino].entries

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