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Proof step 324 from proof refine-rename-dir-negdentry (previous step)

# links(m9, cache_dirs) = cache_dirs[m9].nlink, # links(m16, cache_dirs) = cache_dirs[m16].nlink, # links(entries0[str], cache_dirs) = cache_dirs[entries0[str]].nlink, m0 + 1 = cache_dirs[m9].size, m1 + 1 = cache_dirs[m9].nsubdirs, (m16 = m9 ⊃ mkdir(m2 + 1, md0, m4, m5 + 1, entries[str0, entries0[str]]);mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]])) = mkdir(m13, md7, m14, m15, entries4), (m9 = m16 ⊃ mkdir(m2 + 1, md5, m4, m5 + 1, entries[str0, entries0[str]]);mkdir(m0, md0, cache_dirs[m9].nlink, m1, entries0 -- str)) = mkdir(m, md, m11, m12, entries2), (m16 = m9 ⊃ mkdir(m0, md3, cache_dirs[m9].nlink, m1, entries0 -- str);cache_dirs[m16]) = mkdir(m2, md2, m4, m5, entries), asynced1 ↔ false, asynced0 ↔ false, cache_dirs[m9] = mkdir(m0 + 1, md3, cache_dirs[m9].nlink, m1 + 1, entries0), cache_dirs[m16] = mkdir(cache_dirs[m16].size, md6, cache_dirs[m16].nlink, cache_dirs[m16].nsubdirs, entries3), cache_dirs[entries0[str]] = mkdir(cache_dirs[entries0[str]].size, md8, cache_dirs[entries0[str]].nlink, cache_dirs[entries0[str]].nsubdirs, entries5), entries0[str] = cache_dirs[m9].entries[str], dirs = dirs0[old_ino, dirs0[old_ino].size:= (dirs0[old_ino].size - 1)], dirs0 = cache_dirs[old_ino, cache_dirs[old_ino].entries:= (cache_dirs[old_ino].entries -- mkdentry(str, entries0[str]).name)], new_ino = m16, old_dent = mkdentry(str, entries0[str]), old_ino = m9, afs-cons (cache_dirs [m9, (m9 = m16 ⊃ mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]);mkdir(m0, md3, cache_dirs[m9].nlink, m1, entries0 -- str)).meta:= md0 ] [m16, mkdir(m13, md5, m14, m15, entries4) ], cache_files), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), afs-cons(cache_dirs, cache_files), dcache-cons(cache_dcache, cache_dirs, cache_files), dcache-cons ((cache_dcache -- dentrykey(m9, str))[dentrykey(m16, str0), mkdentry(str0, entries0[str])], cache_dirs [m9, (m9 = m16 ⊃ mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]);mkdir(m0, md3, cache_dirs[m9].nlink, m1, entries0 -- str)).meta:= md0 ] [m16, mkdir(m13, md5, m14, m15, entries4) ], cache_files), icache-cons(cache_icache, cache_dirs, cache_files), icache-cons (cache_icache[m9, mkientry(false, mkinode(m9, md, true, m11, m12, m))][m16, mkientry(false, mkinode(m16, md5, true, m14, m15, m13))], cache_dirs [m9, (m9 = m16 ⊃ mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]);mkdir(m0, md3, cache_dirs[m9].nlink, m1, entries0 -- str)).meta:= md0 ] [m16, mkdir(m13, md5, m14, m15, entries4) ], cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), pcache-cons (cache_pcache, cache_dirs [m9, (m9 = m16 ⊃ mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]);mkdir(m0, md3, cache_dirs[m9].nlink, m1, entries0 -- str)).meta:= md0 ] [m16, mkdir(m13, md5, m14, m15, entries4) ], cache_files), synced(cache_dirs, cache_icache, cache_pcache), synced (cache_dirs [m9, (m9 = m16 ⊃ mkdir(m2 + 1, md2, m4, m5 + 1, entries[str0, entries0[str]]);mkdir(m0, md3, cache_dirs[m9].nlink, m1, entries0 -- str)).meta:= md0 ] [m16, mkdir(m13, md5, m14, m15, entries4) ], cache_icache[m9, mkientry(false, mkinode(m9, md, true, m11, m12, m))][m16, mkientry(false, mkinode(m16, md5, true, m14, m15, m13))], cache_pcache), str ∈ entries0, m16 ∈ cache_dirs, m9 ∈ cache_dirs, entries0[str] ∈ cache_dirs, str ∈ cache_dirs[m9].entries, dirs0[old_ino].size ≥ 1, m16 = m9 → md5 = md0, cache_sync → synced(cache_files, cache_icache, cache_pcache), cache_sync → synced (cache_files, cache_icache[m9, mkientry(false, mkinode(m9, md, true, m11, m12, m))][m16, mkientry(false, mkinode(m16, md5, true, m14, m15, m13))], cache_pcache), links(m16, cache_dirs) ≠ ∅ ∨ m16 = ROOT_INO, links(m9, cache_dirs) ≠ ∅ ∨ m9 = ROOT_INO ⊦ old_dent.dentry?, str0 ∈ cache_dirs[m16].entries, str0 ∈ entries3

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)