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Proof step 206 from proof refine-unlink (previous step)

# links(m3, cache_dirs) = cache_dirs[m3].nlink, # links(entries[str], cache_dirs) = m0 + 1, m9 + 1 = cache_dirs[m3].size, entries[str] = cache_dirs[m3].entries[str], cache_dirs[m3] = mkdir(m9 + 1, md4, cache_dirs[m3].nlink, cache_dirs[m3].nsubdirs, entries), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries[str]] = mkfile(m7, md2, m0 + 1, content0), cache_files[entries[str]] = mkfile(m2, md3, m0 + 1, content), p_ino = m3, afs-cons(cache_dirs, cache_files), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), afs-cons (cache_dirs[m3, mkdir(m9, md1, cache_dirs[m3].nlink, cache_dirs[m3].nsubdirs, entries -- str)], cache_files[entries[str], mkfile(m6, md0, m0, content)]), dcache-cons(cache_dcache, cache_dirs, cache_files), dcache-cons (cache_dcache -- dentrykey(m3, str), cache_dirs[m3, mkdir(m9, md1, cache_dirs[m3].nlink, cache_dirs[m3].nsubdirs, entries -- str)], cache_files[entries[str], mkfile(m6, md0, m0, content)]), icache-cons(cache_icache, cache_dirs, cache_files), icache-cons (cache_icache[entries[str], mkientry(false, mkinode(entries[str], md0, false, m0, 0, m6))] [m3, mkientry(false, mkinode(m3, md1, true, cache_dirs[m3].nlink, cache_dirs[m3].nsubdirs, m9)) ], cache_dirs[m3, mkdir(m9, md1, cache_dirs[m3].nlink, cache_dirs[m3].nsubdirs, entries -- str)], cache_files[entries[str], mkfile(m6, md0, m0, content)]), pcache-cons(cache_pcache, cache_dirs, cache_files), pcache-cons (cache_pcache, cache_dirs[m3, mkdir(m9, md1, cache_dirs[m3].nlink, cache_dirs[m3].nsubdirs, entries -- str)], cache_files[entries[str], mkfile(m6, md0, m0, content)]), synced(cache_dirs, cache_icache, cache_pcache), synced (cache_dirs[m3, mkdir(m9, md1, cache_dirs[m3].nlink, cache_dirs[m3].nsubdirs, entries -- str)], cache_icache[entries[str], mkientry(false, mkinode(entries[str], md0, false, m0, 0, m6))] [m3, mkientry(false, mkinode(m3, md1, true, cache_dirs[m3].nlink, cache_dirs[m3].nsubdirs, m9)) ], cache_pcache), str ∈ cache_dirs[m3].entries, m3 ∈ cache_dirs, entries[str] ∈ cache_files, str ∈ entries, cache_dirs[p_ino, cache_dirs[p_ino].entries:= (cache_dirs[p_ino].entries -- mkdentry(str, entries[str]).name)][p_ino].size ≥ 1, cache_sync → synced(cache_files, cache_icache, cache_pcache), cache_sync → synced (cache_files[entries[str], mkfile(m6, md0, m0, content)], cache_icache[entries[str], mkientry(false, mkinode(entries[str], md0, false, m0, 0, m6))] [m3, mkientry(false, mkinode(m3, md1, true, cache_dirs[m3].nlink, cache_dirs[m3].nsubdirs, m9)) ], cache_pcache), links(m3, cache_dirs) ≠ ∅ ∨ m3 = ROOT_INO ⊦ mkdentry(str, entries[str]).dentry? ∧ str ∈ entries

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

Additional information

Used simplifier rules: ⊦ mkdentry(str, m).dentry?; (s)% ⊦ n ≥ m ↔ m ≤ n; (s)% ⊦ (ad.entries:= entries).size = ad.size; (s)% ⊦ dirs[ino, ad][ino0] = (ino0 = ino ∧ ino ∈ dirs ⊃ ad;dirs[ino0]); (s)% ⊦ mkdentry(str, m).name = str; (s)