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Proof step 284 from proof refine-link (previous step)

# links(m, cache_dirs) = cache_dirs[m].nlink, entries1[str] = cache_dirs[ino2].entries[str], cache_files[entries1[str]] = mkfile(m3, md6, # links(entries1[str], cache_dirs), content1), entries0[str] = entries1[str], cache_dirs[m] = mkdir(cache_dirs[m].size, md4, cache_dirs[m].nlink, cache_dirs[m].nsubdirs, entries2), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries1[str]] = mkfile(m5, md1, # links(entries1[str], cache_dirs), content), cache_dirs[ino] = mkdir(m0, md3, # links(ino, cache_dirs), m2, entries0), cache_dirs[ino0] = mkdir(m4, md2, # links(ino0, cache_dirs), m10, entries), entries[str] = entries1[str], cache_dirs[ino1] = mkdir(m7, md5, # links(ino1, cache_dirs), m11, entries1), p_ino = m, 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 ∈ cache_dirs[ino2].entries, ino2 ∈ cache_dirs, str ∈ entries, str ∈ entries0, ino0 ∈ cache_dirs, ino ∈ cache_dirs, m ∈ cache_dirs, entries1[str] ∈ cache_files, ino1 ∈ cache_dirs, str ∈ entries1, ⌊err0⌋ , cache_sync → synced(cache_files, cache_icache, cache_pcache), links(ino2, cache_dirs) ≠ ∅ ∨ ino2 = ROOT_INO, links(ino0, cache_dirs) ≠ ∅ ∨ ino0 = ROOT_INO, links(ino, cache_dirs) ≠ ∅ ∨ ino = ROOT_INO, links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO, links(ino1, cache_dirs) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ ⟨dirs := cache_dirs[p_ino, cache_dirs[p_ino].entries:= cache_dirs[p_ino].entries[str0, mkdentry(str, entries0[str]).ino]] [p_ino, cache_dirs[p_ino, cache_dirs[p_ino].entries:= cache_dirs[p_ino].entries[str0, mkdentry(str, entries0[str]).ino]][p_ino] .size:= (cache_dirs[p_ino, cache_dirs[p_ino].entries:= cache_dirs[p_ino].entries[str0, mkdentry(str, entries0[str]).ino]][p_ino].size + 1) ]; let ino = mkdentry(str, entries0[str]).ino in {afs_files := (cache_files ⊕ cache_pcache) ⊕ cache_icache; afs_inc_nlink#(ino; dirs, afs_files)}; new_dent := mkdentry(str0, mkdentry(str, entries0[str]).ino); 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(entries1[str], md0, false, # links(entries1[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(mkdentry(str, entries0[str]).ino, 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(entries1[str], md0, false, # links(entries1[str], cache_dirs), 0, m6) = c_inode ∧ negdentry(str0) = new_dent ∧ err0 = err), ⟨fail#(; ; err); asynced := ?⟩ ((asynced ↔ asynced0) ∧ err0 = err), str0 ∈ entries2, str0 ∈ cache_dirs[m].entries

Heuristic symbolic execution applied rule assign right

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: ⊦ mkdentry(str, m).dentry?; (s)