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Proof step 4 from proof refine-create (previous step)

p_inode0.nlink = cache_dirs[p_inode0.ino].nlink, 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, dent = dent0, dent0 = negdentry(str), err = err0, p_inode = p_inode0, p_inode0.directory, 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_inode0.ino ∈ cache_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(p_inode0.ino, cache_dirs) ≠ ∅ ∨ p_inode0.ino = ROOT_INO ⊦ ⟪cache_create#(md; p_inode, c_inode, dent, err, cache_dirs, cache_files, cache_icache, cache_dcache, cache_asynced)⟫ ⟨afs_create#(md; p_inode0, p_inode1, 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 ∧ dent = dent0 ∧ err = err0), str ∈ cache_dirs[p_inode0.ino].entries

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
p_inode0.nlink = cache_dirs[p_inode0.ino].nlink, 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, dent = negdentry(str), err = err0, 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), p_inode0.ino ∈ cache_dirs, ¬ str ∈ cache_dirs[p_inode0.ino].entries, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(p_inode0.ino, cache_dirs) ≠ ∅ ∨ p_inode0.ino = ROOT_INO ⊦ ⟪cache_create#(md; p_inode, c_inode, dent, err, cache_dirs, cache_files, cache_icache, cache_dcache, cache_asynced)⟫ ⟨dent0 := negdentry(str); afs_create#(md; p_inode0, p_inode1, 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 ∧ dent = dent0 ∧ err = err0)

Rule argument

Additional information

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