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Proof step 20 from proof inv-mkdir (previous step)

dirs[m] = mkdir(m0, md1, # links(m, dirs), m2, entries), dent = negdentry(str), p_inode = mkinode(m, md0, true, # links(m, dirs), m2, m0), afs-cons(dirs, files), dcache-cons(dcache, dirs, files), icache-cons(icache, dirs, files), pcache-cons(pcache, dirs, files), synced(dirs, icache, pcache), m ∈ dirs, asynced1 → synced(files, icache, pcache), links(m, dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ [if pre-mkdir(p_inode, dent, md, dirs, files) then { {choose ino with ¬ ino ∈ dirs ∧ ¬ ino ∈ files ∧ ino ≠ 0 in afs_mkdir_ino#(p_inode.ino, md, ino; dent, err, dirs); afs_inode_sync#(p_inode; dirs, files); p_inode := getinode(p_inode.ino, dirs, files); c_inode := getinode(dent.ino, dirs, files)} or fail#(; ; err); asynced := ?} else abort] ( afs-cons(dirs, files) → ⟪if err = ESUCCESS then let asynced = false in {icache_set#(p_inode, asynced; err, icache); icache_set#(c_inode, asynced; err, icache); dcache_set#(p_inode.ino, dent.name, dent; 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)))), str ∈ entries

Heuristic conditional right split applied rule if right

And obtained the following new goals

Rule argument

pos: right 1

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