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Proof step 28 from proof inv-rmdir (previous step)

dirs[entries[str]] = mkdir(m0, md2, # links(entries[str], dirs), m2, ∅), dirs[m] = mkdir(m1, md3, # links(m, dirs), m4, entries), c_inode = mkinode(entries[str], md0, true, # links(entries[str], dirs), m2, m0), dent = mkdentry(str, entries[str]), p_inode = mkinode(m, md, true, # links(m, dirs), m4, m1), afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), entries[str] ∈ dirs, str ∈ entries, m ∈ dirs, asynced1 → synced(files, icache, pcache), links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ [if pre-rmdir(p_inode, c_inode, dent, dirs, files) then { let p_ino = p_inode.ino in {dirs[p_ino].entries := dirs[p_ino].entries -- dent.name; dirs[p_ino].size := dirs[p_ino].size - 1; dirs[p_ino].nsubdirs := dirs[p_ino].nsubdirs - 1; let ino = dent.ino in afs_drop_nlink#(ino; dirs, files); dent := negdentry(dent.name); afs_inode_sync#(p_inode; dirs, files); afs_inode_sync#(c_inode; dirs, files); p_inode := getinode(p_inode.ino, dirs, files); c_inode := getinode(c_inode.ino, dirs, files); err := ESUCCESS} or fail#(; ; err); asynced := ?} else abort] ( 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) ∧ (asynced1 → synced(files, icache, pcache)))), entries[str] = ROOT_INO

Heuristic conditional right split applied rule if right

And obtained the following new goals

Rule argument

pos: right 1

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