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Proof step 25 from proof refine-rename-file-negdentry (previous step)

# links(m3, cache_dirs) = cache_dirs[m3].nlink, # links(m, cache_dirs) = cache_dirs[m].nlink, cache_dirs[m].nlink = m12, cache_dirs[m3].nlink = m1, cache_dirs[m3] = mkdir(cache_dirs[m3].size, md4, cache_dirs[m3].nlink, cache_dirs[m3].nsubdirs, entries0), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries0[str]] = mkfile(m9, md2, m5, content), cache_dirs[m] = mkdir(cache_dirs[m].size, md3, cache_dirs[m].nlink, cache_dirs[m].nsubdirs, entries), entries0[str] = cache_dirs[m3].entries[str], cache_files[entries0[str]] = mkfile(m4, md5, m5, content0), afs_dirs = cache_dirs, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, err = err0, m0 = cache_dirs[m3].size, m11 = m5, m13 = cache_dirs[m].nsubdirs, m2 = cache_dirs[m3].nsubdirs, m8 = cache_dirs[m].size, new_child_inode = new_child_inode0, new_dent = negdentry(str0), new_parent_inode = mkinode(m, md, true, cache_dirs[m].nlink, cache_dirs[m].nsubdirs, cache_dirs[m].size), old_child_inode = mkinode(entries0[str], md1, false, m5, 0, m10), old_dent = mkdentry(str, entries0[str]), old_parent_inode = mkinode(m3, md0, true, cache_dirs[m3].nlink, cache_dirs[m3].nsubdirs, cache_dirs[m3].size), 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, m3 ∈ cache_dirs, entries0[str] ∈ cache_files, m ∈ cache_dirs, str ∈ cache_dirs[m3].entries, m = m3 → md = md0, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m3, cache_dirs) ≠ ∅ ∨ m3 = ROOT_INO, links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪afs_rename#(; old_parent_inode, new_parent_inode, old_child_inode, new_child_inode, old_dent, new_dent, err, cache_dirs, cache_files; asynced1); if err = ESUCCESS then let asynced = false in {icache_set#(old_parent_inode, asynced; err, cache_icache); icache_set#(new_parent_inode, asynced; err, cache_icache); skip; dcache_delete#(old_parent_inode.ino, old_dent.name; err, cache_dcache); dcache_set#(new_parent_inode.ino, new_dent.name, new_dent; err, cache_dcache)}⟫ ⟨old_dent0 := mkdentry(str, entries0[str]); new_dent0 := negdentry(str0); new_parent_inode0 := mkinode(m, md, true, m12, m13, m8); old_parent_inode0 := mkinode(m3, md0, true, m1, m2, m0); old_child_inode0 := mkinode(entries0[str], md1, false, m11, 0, m10); afs_rename# (; old_parent_inode0, new_parent_inode0, old_child_inode0, new_child_inode0, old_dent0, new_dent0, err0, afs_dirs, afs_files; afs_asynced)⟩ ( old_parent_inode = old_parent_inode0 ∧ new_parent_inode = new_parent_inode0 ∧ old_child_inode = old_child_inode0 ∧ new_child_inode = new_child_inode0 ∧ old_dent = old_dent0 ∧ new_dent = new_dent0 ∧ err = err0 ∧ afs_dirs = cache_dirs ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ asynced1)), str0 ∈ cache_dirs[m].entries, str0 ∈ entries

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: 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