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Proof step 271 from proof refine-unlink (previous step)

cache_dirs[m] = mkdir(m0 + 1, md1, # links(m, cache_dirs), m4, entries0), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries0[str]] = mkfile(m7, md2, # links(entries0[str], cache_dirs), content0), cache_files[entries0[str]] = mkfile(m1, md3, # links(entries0[str], cache_dirs), content), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, dirs = cache_dirs[m, mkdir(m0, md1, # links(m, cache_dirs), m4, entries0 -- str)], files = afs_files, ino = mkdentry(str, entries0[str]).ino, mkdentry(str, entries0[str]).dentry?, 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), m ∈ cache_dirs, entries0[str] ∈ cache_files, str ∈ entries0, ⌊err0⌋ , cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟨files[ino].nlink := files[ino].nlink - 1; dent := negdentry(mkdentry(str, entries0[str]).name); afs_inode_sync#(mkinode(m, md, true, # links(m, cache_dirs), m4, m0 + 1); dirs, files); afs_inode_sync#(mkinode(entries0[str], md0, false, # links(entries0[str], cache_dirs), 0, m6); dirs, files); p_inode := (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ); c_inode := getinode(entries0[str], dirs, files); err := ESUCCESS; asynced := ?⟩ ( dirs = cache_dirs ∧ files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (asynced ↔ asynced0) ∧ mkinode(m, md, true, # links(m, cache_dirs), m4, m0 + 1) = p_inode ∧ mkinode(entries0[str], md0, false, # links(entries0[str], cache_dirs), 0, m6) = c_inode ∧ mkdentry(str, entries0[str]) = dent ∧ err0 = err), ⟨fail#(; ; err); asynced := ?⟩ ((asynced ↔ asynced0) ∧ err0 = err)

Heuristic symbolic execution applied rule assign right

And obtained the following new goals

Proof step 272:
cache_files[entries0[str]] = mkfile(m1, md3, # links(entries0[str], cache_dirs), content), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries0[str]] = mkfile(m7, md2, # links(entries0[str], cache_dirs), content0), cache_dirs[m] = mkdir(m0 + 1, md1, # links(m, cache_dirs), m4, entries0), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, dirs = cache_dirs[m, mkdir(m0, md1, # links(m, cache_dirs), m4, entries0 -- str)], files = files0[ino, files0[ino].nlink:= (files0[ino].nlink - 1)], files0 = afs_files, ino = mkdentry(str, entries0[str]).ino, mkdentry(str, entries0[str]).dentry?, 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), str ∈ entries0, entries0[str] ∈ cache_files, m ∈ cache_dirs, files0[ino].nlink ≥ 1, ⌊err0⌋ , cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟨dent := negdentry(mkdentry(str, entries0[str]).name); afs_inode_sync#(mkinode(m, md, true, # links(m, cache_dirs), m4, m0 + 1); dirs, files); afs_inode_sync#(mkinode(entries0[str], md0, false, # links(entries0[str], cache_dirs), 0, m6); dirs, files); p_inode := (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ); c_inode := getinode(entries0[str], dirs, files); err := ESUCCESS; asynced := ?⟩ ( dirs = cache_dirs ∧ files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (asynced ↔ asynced0) ∧ mkinode(m, md, true, # links(m, cache_dirs), m4, m0 + 1) = p_inode ∧ mkinode(entries0[str], md0, false, # links(entries0[str], cache_dirs), 0, m6) = c_inode ∧ mkdentry(str, entries0[str]) = dent ∧ err0 = err), ⟨fail#(; ; err); asynced := ?⟩ ((asynced ↔ asynced0) ∧ err0 = err)

Rule argument

Additional information

Used simplifier rules: ⊦ mkdentry(str, m).dentry?; (s)% ⊦ mkdentry(str, m).ino = m; (s)% ⊦ n ≥ m ↔ m ≤ n; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ m < 1 ↔ m = 0; (s)% ⊦ mkfile(m, md, m0, content).nlink = m0; (s)%size-zero-02: ⊦ # ls = 0 → ls = ∅; (forward) from specification set-basic[alink-set]%⊦ p_ino ∈ dirs ∧ dirs[p_ino] = mkdir(m, md, n, n0, entries) ∧ str ∈ entries → links(entries[str], dirs) ≠ ∅; (s)%⊦ afs-cons(dirs, files) → ( links(ino, dirs) = ∅ ↔ (ino ∈ dirs → dirs[ino].nlink = 0) ∧ (ino ∈ files → files[ino].nlink = 0)); (ws)% ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs → ¬ ino ∈ files; (s)%afs-cons-file-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n, content) → # links(ino, dirs) = n; (forward) from specification afs-base%size-zero-01: ⊦ ls ≠ ∅ → # ls ≠ 0; (forward) from specification set-basic[alink-set]