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Proof step 238 from proof refine-mkdir (previous step)

cache_dirs[m] = mkdir(m0, md1, # links(m, cache_dirs), m2, entries), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, c_inode = p_inode1, cache_dirs0 = cache_dirs, dent0 = negdentry(str), p_inode = mkinode(m, md0, true, # links(m, cache_dirs), m2, m0), p_inode0 = mkinode(m, md0, true, # links(m, cache_dirs), m2, m0), 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, ⌊err0⌋ , ¬ str ∈ entries, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟨afs_mkdir#(md; p_inode0, p_inode1, dent0, err1, cache_dirs, afs_files; afs_asynced)⟩ ( cache_dirs = cache_dirs0 ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ asynced) ∧ p_inode = p_inode0 ∧ c_inode = p_inode1 ∧ negdentry(str) = dent0 ∧ err0 = err1)

Heuristic unfold applied rule call right

And obtained the following new goals

Proof step 239:
cache_dirs[m] = mkdir(m0, md1, # links(m, cache_dirs), m2, entries), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, c_inode = p_inode1, c_inode0 = p_inode1, cache_dirs0 = cache_dirs, dent = dent0, dent0 = negdentry(str), dirs = cache_dirs, err = err1, files = afs_files, p_inode = p_inode0, p_inode0 = mkinode(m, md0, true, # links(m, cache_dirs), m2, m0), p_inode2 = mkinode(m, md0, true, # links(m, cache_dirs), m2, m0), afs-cons(cache_dirs, cache_files), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), 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, ⌊err0⌋ , 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 { {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⟩ ( dirs = cache_dirs0 ∧ files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (asynced ↔ asynced0) ∧ p_inode2 = p_inode ∧ c_inode0 = c_inode ∧ negdentry(str) = dent ∧ err0 = err), str ∈ entries

Rule argument

pos: right 1

Additional information

Used simplifier rules: afs_mkdir#(MD; P_INODE, C_INODE, DENT, ERR, DIRS, FILES; ASYNCED) {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 };