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Proof step 6 from proof refine-link (previous step)

p_inode1.ino = cache_dirs[ino].entries[str], p_inode1.nlink = ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[p_inode1.ino].nlink, p_inode0.nlink = cache_dirs[p_inode0.ino].nlink, p_inode1.nsubdirs = 0, p_inode0.nsubdirs = cache_dirs[p_inode0.ino].nsubdirs, p_inode0.size = cache_dirs[p_inode0.ino].size, afs_dirs = cache_dirs, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, c_inode = p_inode1, err = err0, new_dent = old_dent0, old_dent0 = negdentry(str0), p_inode = p_inode0, p_inode0.directory, old_dent0.negdentry?, afs-cons(cache_dirs, cache_files), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), p_inode1.ino ∈ cache_files, p_inode0.ino ∈ cache_dirs, str ∈ cache_dirs[ino].entries, ino ∈ cache_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(p_inode1.ino, cache_dirs) ≠ ∅ ∨ p_inode1.ino = ROOT_INO, links(p_inode0.ino, cache_dirs) ≠ ∅ ∨ p_inode0.ino = ROOT_INO, links(ino, cache_dirs) ≠ ∅ ∨ ino = ROOT_INO ⊦ ⟪cache_link#(mkdentry(str, p_inode1.ino); p_inode, c_inode, new_dent, err, cache_dirs, cache_files, cache_icache, cache_dcache, cache_asynced)⟫ ⟨afs_link#(mkdentry(str, p_inode1.ino); p_inode0, p_inode1, old_dent0, err0, afs_dirs, afs_files; afs_asynced)⟩ ( afs_dirs = cache_dirs ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ cache_asynced) ∧ p_inode = p_inode0 ∧ c_inode = p_inode1 ∧ new_dent = old_dent0 ∧ err = err0), p_inode1.directory, str0 ∈ cache_dirs[p_inode0.ino].entries

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
p_inode1.ino = cache_dirs[ino].entries[str], p_inode0.nlink = cache_dirs[p_inode0.ino].nlink, p_inode1.nlink = ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[p_inode1.ino].nlink, p_inode0.nsubdirs = cache_dirs[p_inode0.ino].nsubdirs, p_inode1.nsubdirs = 0, p_inode0.size = cache_dirs[p_inode0.ino].size, afs_dirs = cache_dirs, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, c_inode = p_inode1, err = err0, new_dent = negdentry(str0), p_inode = p_inode0, p_inode0.directory, afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), afs-cons(cache_dirs, cache_files), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), ino ∈ cache_dirs, str ∈ cache_dirs[ino].entries, p_inode0.ino ∈ cache_dirs, p_inode1.ino ∈ cache_files, ¬ p_inode1.directory, ¬ str0 ∈ cache_dirs[p_inode0.ino].entries, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(ino, cache_dirs) ≠ ∅ ∨ ino = ROOT_INO, links(p_inode0.ino, cache_dirs) ≠ ∅ ∨ p_inode0.ino = ROOT_INO, links(p_inode1.ino, cache_dirs) ≠ ∅ ∨ p_inode1.ino = ROOT_INO ⊦ ⟪cache_link#(mkdentry(str, p_inode1.ino); p_inode, c_inode, new_dent, err, cache_dirs, cache_files, cache_icache, cache_dcache, cache_asynced)⟫ ⟨old_dent0 := negdentry(str0); afs_link#(mkdentry(str, p_inode1.ino); p_inode0, p_inode1, old_dent0, err0, afs_dirs, afs_files; afs_asynced)⟩ ( afs_dirs = cache_dirs ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ cache_asynced) ∧ p_inode = p_inode0 ∧ c_inode = p_inode1 ∧ new_dent = old_dent0 ∧ err = err0)

Rule argument

Additional information

Used simplifier rules: ⊦ negdentry(str).negdentry?; (s)