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Proof step 245 from proof refine-rmdir (previous step)

# links(m6, cache_dirs) = cache_dirs[m6].nlink, # links(entries0[str], cache_dirs) = cache_dirs[entries0[str]].nlink, m0 + 1 = cache_dirs[m6].size, m1 + 1 = cache_dirs[m6].nsubdirs, cache_dirs[entries0[str]].entries = ∅, (entries0[str] = m6 ⊃ mkdir(m5, md, m3, m7, entries);mkdir(m5, md2, m3, m7, entries)) = mkdir(m, md4, m8, m9, entries1), (entries0[str] = m6 ⊃ mkdir(m0, md1, cache_dirs[entries0[str]].nlink, m1, entries0 -- str);cache_dirs[entries0[str]]) = mkdir(m5, md2, m3 + 1, m7, entries), (m6 = entries0[str] ⊃ mkdir(m5, md0, m3, m7, entries);mkdir(m0, md, cache_dirs[m6].nlink, m1, entries0 -- str)) = mkdir(m10, md5, m11, m12, entries2), cache_dirs[entries0[str]] = mkdir(cache_dirs[entries0[str]].size, md3, cache_dirs[entries0[str]].nlink, cache_dirs[entries0[str]].nsubdirs, ∅), cache_dirs[m6] = mkdir(m0 + 1, md1, cache_dirs[m6].nlink, m1 + 1, entries0), entries0[str] = cache_dirs[m6].entries[str], p_ino = m6, afs-cons (cache_dirs[m6, (m6 = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md1, cache_dirs[m6].nlink, m1, entries0 -- str)).meta:= md] [entries0[str], mkdir(m, md0, m8, m9, entries1) ], cache_files), afs-cons(cache_dirs, cache_files), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), dcache-cons (cache_dcache -- dentrykey(m6, str), cache_dirs[m6, (m6 = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md1, cache_dirs[m6].nlink, m1, entries0 -- str)).meta:= md] [entries0[str], mkdir(m, md0, m8, m9, entries1) ], cache_files), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons (cache_icache[entries0[str], mkientry(false, mkinode(entries0[str], md0, true, m8, m9, m))] [m6, mkientry(false, mkinode(m6, md5, true, m11, m12, m10)) ], cache_dirs[m6, (m6 = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md1, cache_dirs[m6].nlink, m1, entries0 -- str)).meta:= md] [entries0[str], mkdir(m, md0, m8, m9, entries1) ], cache_files), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons (cache_pcache, cache_dirs[m6, (m6 = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md1, cache_dirs[m6].nlink, m1, entries0 -- str)).meta:= md] [entries0[str], mkdir(m, md0, m8, m9, entries1) ], cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), synced (cache_dirs[m6, (m6 = entries0[str] ⊃ mkdir(m5, md2, m3, m7, entries);mkdir(m0, md1, cache_dirs[m6].nlink, m1, entries0 -- str)).meta:= md] [entries0[str], mkdir(m, md0, m8, m9, entries1) ], cache_icache[entries0[str], mkientry(false, mkinode(entries0[str], md0, true, m8, m9, m))] [m6, mkientry(false, mkinode(m6, md5, true, m11, m12, m10)) ], cache_pcache), str ∈ entries0, m6 ∈ cache_dirs, entries0[str] ∈ cache_dirs, str ∈ cache_dirs[m6].entries, cache_dirs[p_ino, cache_dirs[p_ino].entries:= (cache_dirs[p_ino].entries -- mkdentry(str, entries0[str]).name)][p_ino].size ≥ 1, cache_dirs[p_ino, cache_dirs[p_ino].entries:= (cache_dirs[p_ino].entries -- mkdentry(str, entries0[str]).name)] [p_ino, cache_dirs[p_ino, cache_dirs[p_ino].entries:= (cache_dirs[p_ino].entries -- mkdentry(str, entries0[str]).name)][p_ino] .size:= (cache_dirs[p_ino, cache_dirs[p_ino].entries:= (cache_dirs[p_ino].entries -- mkdentry(str, entries0[str]).name)][p_ino].size - 1) ] [p_ino ] .nsubdirs ≥ 1, cache_sync → synced (cache_files, cache_icache[entries0[str], mkientry(false, mkinode(entries0[str], md0, true, m8, m9, m))] [m6, mkientry(false, mkinode(m6, md5, true, m11, m12, m10)) ], cache_pcache), cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m6, cache_dirs) ≠ ∅ ∨ m6 = ROOT_INO ⊦ entries0[str] = ROOT_INO, mkdentry(str, entries0[str]).dentry? ∧ str ∈ entries0

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).nsubdirs = ad.nsubdirs; (s)% ⊦ (ad.size:= m).nsubdirs = ad.nsubdirs; (s)% ⊦ dirs[ino, ad][ino, ad0] = dirs[ino, ad0]; (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)