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Proof step 305 from proof refine-rmdir (previous step)

cache_dirs[entries[str]] = mkdir(m2, md1, # links(entries[str], cache_dirs), m4, ∅), cache_dirs[m] = mkdir(m0 + 1, md2, # links(m, cache_dirs), m1 + 1, entries), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, dirs = dirs0[ino, dirs0[ino].nlink:= (dirs0[ino].nlink - 1)], dirs0 = cache_dirs[m, mkdir(m0, md2, # links(m, cache_dirs), m1, entries -- str)], files = afs_files, ino = mkdentry(str, entries[str]).ino, mkdentry(str, entries[str]).dentry?, 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), str ∈ entries, m ∈ cache_dirs, entries[str] ∈ cache_dirs, dirs0[ino].nlink ≥ 1, ⌊err0⌋ , cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟨afs_inode_sync#(mkinode(m, md, true, # links(m, cache_dirs), m1 + 1, m0 + 1); dirs, files); afs_inode_sync#(mkinode(entries[str], md0, true, # links(entries[str], cache_dirs), m4, m2); dirs, files); p_inode := (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode(m, files[m].meta, false, files[m].nlink, 0, files[m].size) ); c_inode := getinode(entries[str], dirs, files); err := ESUCCESS; asynced := ?⟩ ( dirs = cache_dirs ∧ files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (asynced ↔ asynced0) ∧ mkinode(m, md, true, # links(m, cache_dirs), m1 + 1, m0 + 1) = p_inode ∧ mkinode(entries[str], md0, true, # links(entries[str], cache_dirs), m4, m2) = c_inode ∧ mkdentry(str, entries[str]) = negdentry(mkdentry(str, entries[str]).name) ∧ err0 = err), ⟨fail#(; ; err); asynced := ?⟩ ((asynced ↔ asynced0) ∧ err0 = err), entries[str] = ROOT_INO

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 306:
cache_dirs[entries[str]] = mkdir(m2, md1, # links(entries[str], cache_dirs), m4, ∅), cache_dirs[m] = mkdir(m0 + 1, md2, # links(m, cache_dirs), m1 + 1, entries), (entries[str] = m ⊃ mkdir(m0, md2, # links(entries[str], cache_dirs), m1, entries -- str) ;mkdir(m2, md1, # links(entries[str], cache_dirs), m4, ∅) ) .nlink ≠ 0, entries[str] ≠ ROOT_INO, 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), str ∈ entries, m ∈ cache_dirs, entries[str] ∈ cache_dirs, 1 ≤ (entries[str] = m ⊃ mkdir(m0, md2, # links(entries[str], cache_dirs), m1, entries -- str) ;mkdir(m2, md1, # links(entries[str], cache_dirs), m4, ∅) ) .nlink, ⌊err0⌋ , cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ ⟨fail#(; ; err); asynced := ?⟩ ((asynced ↔ asynced0) ∧ err0 = err)

Rule argument

Additional information

Used simplifier rules: not-zero: 0 < n ⊦ (* n) ≤ m → m ≠ 0; (forward) from specification nat% ⊦ mkdentry(str, m) ≠ negdentry(str0); (s)% ⊦ mkdentry(str, m).name = str; (s)% ⊦ mkdentry(str, m).dentry?; (s)% ⊦ n ≥ m ↔ m ≤ n; (s)% ⊦ dirs[ino, ad][ino0] = (ino0 = ino ∧ ino ∈ dirs ⊃ ad;dirs[ino0]); (s)% ⊦ mkdentry(str, m).ino = m; (s)