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Proof step 46 from proof inv-rename-dir-dentry (previous step)

# links(entries2[str], dirs) = m2, # links(entries0[str0], dirs) = dirs[entries0[str0]].nlink, # links(m, dirs) = dirs[m].nlink, # links(m0, dirs) = dirs[m0].nlink, dirs[entries0[str0]] = mkdir(dirs[entries0[str0]].size, md4, dirs[entries0[str0]].nlink, dirs[entries0[str0]].nsubdirs, entries), dirs[entries2[str]] = mkdir(m1, md7, m2, m3, ∅), dirs[m] = mkdir(dirs[m].size, md3, dirs[m].nlink, dirs[m].nsubdirs, entries2), dirs[m0] = mkdir(dirs[m0].size, md5, dirs[m0].nlink, dirs[m0].nsubdirs, entries0), entries2[str] = dirs[m].entries[str], entries0[str0] = dirs[m0].entries[str0], dirs[entries2[str]] = mkdir(m1, md6, m2, m3, entries1), entries1 = ∅, new_child_inode = mkinode(entries2[str], md, true, m2, m3, m1), new_dent = mkdentry(str, entries2[str]), new_parent_inode = mkinode(m, md1, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size), old_child_inode = mkinode(entries0[str0], md0, true, dirs[entries0[str0]].nlink, dirs[entries0[str0]].nsubdirs, dirs[entries0[str0]].size), old_dent = mkdentry(str0, entries0[str0]), old_parent_inode = mkinode(m0, md2, true, dirs[m0].nlink, dirs[m0].nsubdirs, dirs[m0].size), afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), str0 ∈ entries0, entries2[str] ∈ dirs, entries0[str0] ∈ dirs, m ∈ dirs, m0 ∈ dirs, str ∈ entries2, str ∈ dirs[m].entries, str0 ∈ dirs[m0].entries, asynced → synced(files, icache, pcache), m = m0 → md1 = md2, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO, links(m0, dirs) ≠ ∅ ∨ m0 = ROOT_INO ⊦ [afs_rename#(; old_parent_inode, new_parent_inode, old_child_inode, new_child_inode, old_dent, new_dent, err, dirs, files; asynced1)] ( afs-cons(dirs, files) → ⟪if err = ESUCCESS then let asynced = false in {icache_set#(old_parent_inode, asynced; err, icache); icache_set#(new_parent_inode, asynced; err, icache); if true then icache_set#(new_child_inode, asynced; err, icache); dcache_delete#(old_parent_inode.ino, old_dent.name; err, dcache); dcache_set#(new_parent_inode.ino, new_dent.name, new_dent; err, dcache)}⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced → synced(files, icache, pcache)))), entries2[str] = ROOT_INO

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 47:
# links(m0, dirs) = dirs[m0].nlink, # links(m, dirs) = dirs[m].nlink, # links(entries0[str0], dirs) = dirs[entries0[str0]].nlink, entries0[str0] = dirs[m0].entries[str0], entries2[str] = dirs[m].entries[str], dirs[m0] = mkdir(dirs[m0].size, md5, dirs[m0].nlink, dirs[m0].nsubdirs, entries0), dirs[m] = mkdir(dirs[m].size, md3, dirs[m].nlink, dirs[m].nsubdirs, entries2), dirs[entries2[str]] = mkdir(m1, md6, # links(entries2[str], dirs), m3, ∅), dirs[entries0[str0]] = mkdir(dirs[entries0[str0]].size, md4, dirs[entries0[str0]].nlink, dirs[entries0[str0]].nsubdirs, entries), new_child_inode = mkinode(entries2[str], md, true, # links(entries2[str], dirs), m3, m1), new_dent = mkdentry(str, entries2[str]), new_parent_inode = mkinode(m, md1, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size), old_child_inode = mkinode(entries0[str0], md0, true, dirs[entries0[str0]].nlink, dirs[entries0[str0]].nsubdirs, dirs[entries0[str0]].size), old_dent = mkdentry(str0, entries0[str0]), old_parent_inode = mkinode(m0, md2, true, dirs[m0].nlink, dirs[m0].nsubdirs, dirs[m0].size), entries2[str] ≠ ROOT_INO, afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), str0 ∈ dirs[m0].entries, str ∈ dirs[m].entries, str ∈ entries2, m0 ∈ dirs, m ∈ dirs, entries0[str0] ∈ dirs, entries2[str] ∈ dirs, str0 ∈ entries0, m = m0 → md1 = md2, asynced → synced(files, icache, pcache), links(m0, dirs) ≠ ∅ ∨ m0 = ROOT_INO, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ [afs_rename#(; old_parent_inode, new_parent_inode, old_child_inode, new_child_inode, old_dent, new_dent, err, dirs, files; asynced1)] ( afs-cons(dirs, files) → ⟪if err = ESUCCESS then let asynced = false in {icache_set#(old_parent_inode, asynced; err, icache); icache_set#(new_parent_inode, asynced; err, icache); if true then icache_set#(new_child_inode, asynced; err, icache); dcache_delete#(old_parent_inode.ino, old_dent.name; err, dcache); dcache_set#(new_parent_inode.ino, new_dent.name, new_dent; err, dcache)}⟫ ( icache-cons(icache, dirs, files) ∧ dcache-cons(dcache, dirs, files) ∧ pcache-cons(pcache, dirs, files) ∧ synced(dirs, icache, pcache) ∧ (asynced → synced(files, icache, pcache))))

Rule argument

Additional information

Used simplifier rules: ⊦ mkdir(m, md, m0, m1, entries) = mkdir(m2, md0, m3, m4, entries0) ↔ m = m2 ∧ md = md0 ∧ m0 = m3 ∧ m1 = m4 ∧ entries = entries0; (ws)