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Proof step 244 from proof refine-mkdir (previous step)

# links(m, cache_dirs) = cache_dirs[m].nlink, cache_dirs[m] = mkdir(cache_dirs[m].size, md1, cache_dirs[m].nlink, cache_dirs[m].nsubdirs, entries), cache_dirs0 = cache_dirs, dent = negdentry(str), p_inode = mkinode(m, md0, true, cache_dirs[m].nlink, cache_dirs[m].nsubdirs, cache_dirs[m].size), 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⌋ , ¬ str ∈ entries, ¬ str ∈ cache_dirs[m].entries, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟨fail#(; ; err); asynced := ?⟩ ((asynced ↔ asynced0) ∧ err0 = err), ∃ ino. ¬ ino ∈ cache_dirs ∧ ¬ ino ∈ cache_files ∧ ino ≠ 0 ∧ ⟨afs_mkdir_ino#(m, md, ino; dent, err, cache_dirs); afs_files := (cache_files ⊕ cache_pcache) ⊕ cache_icache; afs_inode_sync#(p_inode; cache_dirs, afs_files); p_inode2 := (p_inode.ino ∈ cache_dirs ⊃ mkinode (p_inode.ino, cache_dirs[p_inode.ino].meta, true, cache_dirs[p_inode.ino].nlink, cache_dirs[p_inode.ino].nsubdirs, cache_dirs[p_inode.ino].size) ;mkinode(p_inode.ino, afs_files[p_inode.ino].meta, false, afs_files[p_inode.ino].nlink, 0, afs_files[p_inode.ino].size) ); c_inode := getinode(dent.ino, cache_dirs, afs_files); asynced := ?⟩ ( cache_dirs = cache_dirs0 ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (asynced ↔ asynced0) ∧ p_inode = p_inode2 ∧ p_inode1 = c_inode ∧ negdentry(str) = dent ∧ err0 = err)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 245:
# links(m, cache_dirs) = cache_dirs[m].nlink, cache_dirs[m] = mkdir(cache_dirs[m].size, md1, cache_dirs[m].nlink, cache_dirs[m].nsubdirs, entries), cache_dirs0 = cache_dirs, dent = negdentry(str), p_inode = mkinode(m, md0, true, cache_dirs[m].nlink, cache_dirs[m].nsubdirs, cache_dirs[m].size), p_inode = mkinode(m0, md2, boolvar, m1, m2, 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, ⌊err0⌋ , cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟨fail#(; ; err); asynced := ?⟩ ((asynced ↔ asynced0) ∧ err0 = err), ∃ ino. ¬ ino ∈ cache_dirs ∧ ¬ ino ∈ cache_files ∧ ino ≠ 0 ∧ ⟨afs_mkdir_ino#(m, md, ino; dent, err, cache_dirs); afs_files := (cache_files ⊕ cache_pcache) ⊕ cache_icache; afs_inode_sync#(p_inode; cache_dirs, afs_files); p_inode2 := (m0 ∈ cache_dirs ⊃ mkinode(m0, cache_dirs[m0].meta, true, cache_dirs[m0].nlink, cache_dirs[m0].nsubdirs, cache_dirs[m0].size) ;mkinode(m0, afs_files[m0].meta, false, afs_files[m0].nlink, 0, afs_files[m0].size) ); c_inode := getinode(dent.ino, cache_dirs, afs_files); asynced := ?⟩ ( cache_dirs = cache_dirs0 ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (asynced ↔ asynced0) ∧ p_inode = p_inode2 ∧ p_inode1 = c_inode ∧ negdentry(str) = dent ∧ err0 = err), str ∈ entries, str ∈ cache_dirs[m].entries

Rule argument

spec: inode name: elim seq: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2) subst: [inode, m, md, boolvar, m0, m1, m2] → [p_inode, m0, md2, boolvar, m1, m2, m3]

Additional information

Used simplifier rules: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2); (elim) Used terms: p_inode, m0, md2, boolvar, m1, m2, m3