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Proof step 24 from proof inv-rmdir (previous step)

# links(m, dirs) = dirs[m].nlink, # links(entries0[str], dirs) = m1, dirs[entries0[str]] = mkdir(m0, md3, m1, m2, ∅), dirs[m] = mkdir(dirs[m].size, md1, dirs[m].nlink, dirs[m].nsubdirs, entries0), entries0[str] = dirs[m].entries[str], dirs[entries0[str]] = mkdir(m0, md2, m1, m2, entries), c_inode = mkinode(entries0[str], md0, true, m1, m2, m0), dent = mkdentry(str, entries0[str]), entries = ∅, p_inode = mkinode(m, md, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size), afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), entries0[str] ∈ dirs, str ∈ entries0, m ∈ dirs, str ∈ dirs[m].entries, asynced → synced(files, icache, pcache), links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ [afs_rmdir#(; p_inode, c_inode, dent, err, dirs, files; asynced0)] ( afs-cons(dirs, files) → ⟪if err = ESUCCESS then let asynced = false in {icache_set#(c_inode, asynced; err, icache); icache_set#(p_inode, asynced; err, icache); dcache_delete#(p_inode.ino, dent.name; 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)))), entries0[str] = ROOT_INO

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 25:
# links(m, dirs) = dirs[m].nlink, entries0[str] = dirs[m].entries[str], dirs[m] = mkdir(dirs[m].size, md1, dirs[m].nlink, dirs[m].nsubdirs, entries0), dirs[entries0[str]] = mkdir(m0, md2, # links(entries0[str], dirs), m2, ∅), c_inode = mkinode(entries0[str], md0, true, # links(entries0[str], dirs), m2, m0), dent = mkdentry(str, entries0[str]), p_inode = mkinode(m, md, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size), entries0[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), str ∈ dirs[m].entries, m ∈ dirs, str ∈ entries0, entries0[str] ∈ dirs, asynced → synced(files, icache, pcache), links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ [afs_rmdir#(; p_inode, c_inode, dent, err, dirs, files; asynced0)] ( afs-cons(dirs, files) → ⟪if err = ESUCCESS then let asynced = false in {icache_set#(c_inode, asynced; err, icache); icache_set#(p_inode, asynced; err, icache); dcache_delete#(p_inode.ino, dent.name; 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)