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Proof step 255 from proof refine-unlink (previous step)

cache_dirs[m] = mkdir(m0, md4, # links(m, cache_dirs), m3, entries), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries[str]] = mkfile(m7, md2, # links(entries[str], cache_dirs), content0), cache_files[entries[str]] = mkfile(m1, md3, # links(entries[str], cache_dirs), content), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, c_inode = p_inode1, c_inode0 = mkinode(entries[str], md0, false, # links(entries[str], cache_dirs), 0, m6), cache_dirs0 = cache_dirs, dent = dent0, dent0 = mkdentry(str, entries[str]), dirs = cache_dirs, err = err1, files = afs_files, p_inode = p_inode0, p_inode0 = mkinode(m, md, true, # links(m, cache_dirs), m3, m0), p_inode1 = mkinode(entries[str], md0, false, # links(entries[str], cache_dirs), 0, m6), p_inode2 = mkinode(m, md, true, # links(m, cache_dirs), m3, m0), 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), pre-unlink(p_inode, c_inode, dent, dirs, files), synced(cache_dirs, cache_icache, cache_pcache), str ∈ entries, m ∈ cache_dirs, entries[str] ∈ cache_files, ⌊err0⌋ , cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟨fail#(; ; err); asynced := ?⟩ ( dirs = cache_dirs0 ∧ files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (asynced ↔ asynced0) ∧ p_inode2 = p_inode ∧ c_inode0 = c_inode ∧ mkdentry(str, entries[str]) = dent ∧ err0 = err), ⟨let p_ino = p_inode.ino in {dirs[p_ino].entries := dirs[p_ino].entries -- dent.name; dirs[p_ino].size := dirs[p_ino].size - 1; let ino = dent.ino in afs_drop_nlink#(ino; dirs, files); dent := negdentry(dent.name); afs_inode_sync#(p_inode; dirs, files); afs_inode_sync#(c_inode; dirs, files); p_inode := getinode(p_inode.ino, dirs, files); c_inode := getinode(c_inode.ino, dirs, files); err := ESUCCESS}; asynced := ?⟩ ( dirs = cache_dirs0 ∧ files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (asynced ↔ asynced0) ∧ p_inode2 = p_inode ∧ c_inode0 = c_inode ∧ mkdentry(str, entries[str]) = dent ∧ err0 = err)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 256:
# links(m, cache_dirs) = cache_dirs[m].nlink, entries[str] = cache_dirs[m].entries[str], cache_dirs[m] = mkdir(cache_dirs[m].size, md4, cache_dirs[m].nlink, cache_dirs[m].nsubdirs, entries), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries[str]] = mkfile(m7, md2, # links(entries[str], cache_dirs), content0), cache_files[entries[str]] = mkfile(m1, md3, # links(entries[str], cache_dirs), content), 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), str ∈ cache_dirs[m].entries, str ∈ entries, m ∈ cache_dirs, entries[str] ∈ cache_files, ⌊err0⌋ , cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟨let p_ino = m in {dirs := cache_dirs[p_ino, cache_dirs[p_ino].entries:= (cache_dirs[p_ino].entries -- mkdentry(str, entries[str]).name)]; dirs[p_ino].size := dirs[p_ino].size - 1; let ino = mkdentry(str, entries[str]).ino in {afs_files := (cache_files ⊕ cache_pcache) ⊕ cache_icache; afs_drop_nlink#(ino; dirs, afs_files)}; dent := negdentry(mkdentry(str, entries[str]).name); afs_inode_sync#(mkinode(m, md, true, # links(m, cache_dirs), cache_dirs[m].nsubdirs, cache_dirs[m].size); dirs, afs_files); afs_inode_sync#(mkinode(entries[str], md0, false, # links(entries[str], cache_dirs), 0, m6); dirs, afs_files); p_inode := (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode(m, afs_files[m].meta, false, afs_files[m].nlink, 0, afs_files[m].size) ); c_inode := getinode(entries[str], dirs, afs_files); err := ESUCCESS}; asynced := ?⟩ ( dirs = cache_dirs ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (asynced ↔ asynced0) ∧ mkinode(m, md, true, # links(m, cache_dirs), cache_dirs[m].nsubdirs, cache_dirs[m].size) = p_inode ∧ mkinode(entries[str], md0, false, # links(entries[str], cache_dirs), 0, m6) = c_inode ∧ mkdentry(str, entries[str]) = dent ∧ err0 = err), ⟨fail#(; ; err); asynced := ?⟩ ((asynced ↔ asynced0) ∧ err0 = err)

Rule argument

Additional information

Used simplifier rules: ⊦ mkfile(m, md, m0, content).nlink = m0; (s)%⊦ getinode(ino, dirs, files) = (ino ∈ dirs ⊃ mkinode (ino, dirs[ino].meta, true, dirs[ino].nlink, dirs[ino].nsubdirs, dirs[ino].size) ;mkinode (ino, files[ino].meta, false, files[ino].nlink, 0, files[ino].size) ); (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (s)% ⊦ valid-dir-ino(ino, dirs, files) ↔ ino ∈ dirs; (s)%⊦ valid-dir-inode(inode, dirs, files) ↔ valid-dir-ino(inode.ino, dirs, files) ∧ inode.nlink = dirs[inode.ino].nlink ∧ inode.size = dirs[inode.ino].size ∧ inode.nsubdirs = dirs[inode.ino].nsubdirs ∧ inode.directory; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nsubdirs = m1; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).nlink = m0; (s)% ⊦ valid-file-ino(ino, dirs, files) ↔ ino ∈ files; (s)%⊦ valid-file-inode(inode, dirs, files) ↔ valid-file-ino(inode.ino, dirs, files) ∧ inode.nlink = files[inode.ino].nlink ∧ inode.nsubdirs = 0 ∧ ¬ inode.directory; (s)% ⊦ mkdentry(str, m).dentry?; (s)% ⊦ mkdentry(str, m).name = str; (s)% ⊦ ino ∈ files ⊕ pcache ↔ ino ∈ files; (s)% ⊦ ino ∈ files ⊕ icache ↔ ino ∈ files; (s)% ⊦ valid-ino(ino, dirs, files) ↔ ino ∈ dirs ∨ ino ∈ files; (s)% ⊦ mkdentry(str, m).ino = m; (s)%⊦ valid-parent-ino(ino, dirs, files) ↔ ino ∈ dirs ∧ (links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO); (s)%⊦ valid-dentry(ino, dent, dirs, files) ↔ valid-parent-ino(ino, dirs, files) ∧ valid-ino(dent.ino, dirs, files) ∧ dent.name ∈ dirs[ino].entries ∧ dent.ino = dirs[ino].entries[dent.name] ∧ dent.dentry?; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)%⊦ pre-unlink(p_inode, c_inode, dent, dirs, files) ↔ valid-dentry(p_inode.ino, dent, dirs, files) ∧ valid-file-inode(c_inode, dirs, files) ∧ valid-dir-inode(p_inode, dirs, files) ∧ c_inode.ino = dent.ino; (s)