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Proof step 10 from proof refine-mkdir (previous step)

# links(m, cache_dirs) = m4, asynced0 ↔ cache_asynced, cache_dirs[m] = mkdir(m3, md1, # links(m, cache_dirs), m5, entries), afs_dirs = cache_dirs, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, c_inode = p_inode1, dcache = cache_dcache, dent = negdentry(str), dirs = cache_dirs, err = err0, files = cache_files, icache = cache_icache, p_inode = mkinode(m, md0, true, # links(m, cache_dirs), m5, m3), 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), m ∈ cache_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟪if pre-mkdir(p_inode, dent, md, dirs, files) then {afs_mkdir#(md; p_inode, c_inode, dent, err, dirs, files; asynced0); 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)}} else abort⟫ ⟨dent0 := negdentry(str); p_inode0 := mkinode(m, md0, true, m4, m5, m3); afs_mkdir#(md; p_inode0, p_inode1, dent0, err0, afs_dirs, afs_files; afs_asynced)⟩ ( afs_dirs = dirs ∧ afs_files = (files ⊕ cache_pcache) ⊕ icache ∧ (afs_asynced ↔ asynced0) ∧ p_inode = p_inode0 ∧ c_inode = p_inode1 ∧ dent = dent0 ∧ err = err0), 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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