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Proof step 30 from proof refine-unlink (previous step)

p_inode1.ino = dent0.ino, dent0.ino = cache_dirs[p_inode0.ino].entries[dent0.name], p_inode1.nlink = ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[dent0.ino].nlink, p_inode0.nlink = cache_dirs[p_inode0.ino].nlink, p_inode1.nlink = cache_files[dent0.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, dent = dent0, err = err0, p_inode = p_inode0, dent0.dentry?, 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), dent0.ino ∈ cache_files, dent0.name ∈ cache_dirs[p_inode0.ino].entries, p_inode0.ino ∈ cache_dirs, ¬ p_inode1.directory, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(p_inode0.ino, cache_dirs) ≠ ∅ ∨ p_inode0.ino = ROOT_INO ⊦ [cache_unlink#(; p_inode, c_inode, dent, err, cache_dirs, cache_files, cache_icache, cache_dcache, cache_asynced)] ( icache-cons(cache_icache, cache_dirs, cache_files) ∧ dcache-cons(cache_dcache, cache_dirs, cache_files) ∧ pcache-cons(cache_pcache, cache_dirs, cache_files) ∧ synced(cache_dirs, cache_icache, cache_pcache) ∧ (cache_sync → synced(cache_files, cache_icache, cache_pcache)) ∧ afs-cons(cache_dirs, cache_files) → ⟨afs_unlink#(; 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))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 31:
p_inode1.ino = m, p_inode1.nlink = cache_files[m].nlink, p_inode0.nlink = cache_dirs[p_inode0.ino].nlink, p_inode1.nlink = ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m].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, dent = dent0, dent0 = mkdentry(str, m), err = err0, m = cache_dirs[p_inode0.ino].entries[str], p_inode = p_inode0, dent0.dentry?, p_inode0.directory, 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, str ∈ cache_dirs[p_inode0.ino].entries, m ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(p_inode0.ino, cache_dirs) ≠ ∅ ∨ p_inode0.ino = ROOT_INO ⊦ [cache_unlink#(; p_inode, c_inode, dent, err, cache_dirs, cache_files, cache_icache, cache_dcache, cache_asynced)] ( icache-cons(cache_icache, cache_dirs, cache_files) ∧ dcache-cons(cache_dcache, cache_dirs, cache_files) ∧ pcache-cons(cache_pcache, cache_dirs, cache_files) ∧ synced(cache_dirs, cache_icache, cache_pcache) ∧ (cache_sync → synced(cache_files, cache_icache, cache_pcache)) ∧ afs-cons(cache_dirs, cache_files) → ⟨afs_unlink#(; 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)), p_inode1.directory

Rule argument

spec: dentry name: elim seq: ⊦ dent.dentry? → (str = dent.name ∧ m = dent.ino ↔ dent = mkdentry(str, m)) subst: [dent, str, m] → [dent0, str, m]

Additional information

Used simplifier rules: ⊦ dent.dentry? → (str = dent.name ∧ m = dent.ino ↔ dent = mkdentry(str, m)); (elim) Used terms: dent0, str, m