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Proof step 205 from proof refine-unlink (previous step)

# links(entries0[str], cache_dirs) = m0 + 1, cache_files[entries0[str]] = mkfile(m2, md3, m0 + 1, content), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries0[str]] = mkfile(m7, md2, m0 + 1, content0), cache_dirs[m3] = mkdir(m9 + 1, md, # links(m3, cache_dirs), m4, entries0), dirs = cache_dirs[m3, mkdir(m9, md, # links(m3, cache_dirs), m4, entries0 -- str)], files = ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries0[str], mkfile(m7, md2, m0, content0)], ino = inode.ino, inode = mkinode(m3, md1, true, # links(m3, cache_dirs), m4, m9 + 1), afs-cons(cache_dirs[m3, mkdir(m9, md1, # links(m3, cache_dirs), m4, entries0 -- str)], cache_files[entries0[str], mkfile(m6, md0, m0, content)]), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), afs-cons(cache_dirs, cache_files), dcache-cons (cache_dcache -- dentrykey(m3, str), cache_dirs[m3, mkdir(m9, md1, # links(m3, cache_dirs), m4, entries0 -- str)], cache_files[entries0[str], mkfile(m6, md0, m0, content)]), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons (cache_icache[entries0[str], mkientry(false, mkinode(entries0[str], md0, false, m0, 0, m6))] [m3, mkientry(false, mkinode(m3, md1, true, # links(m3, cache_dirs), m4, m9)) ], cache_dirs[m3, mkdir(m9, md1, # links(m3, cache_dirs), m4, entries0 -- str)], cache_files[entries0[str], mkfile(m6, md0, m0, content)]), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons (cache_pcache, cache_dirs[m3, mkdir(m9, md1, # links(m3, cache_dirs), m4, entries0 -- str)], cache_files[entries0[str], mkfile(m6, md0, m0, content)]), pcache-cons(cache_pcache, cache_dirs, cache_files), synced (cache_dirs[m3, mkdir(m9, md1, # links(m3, cache_dirs), m4, entries0 -- str)], cache_icache[entries0[str], mkientry(false, mkinode(entries0[str], md0, false, m0, 0, m6))] [m3, mkientry(false, mkinode(m3, md1, true, # links(m3, cache_dirs), m4, m9)) ], cache_pcache), synced(cache_dirs, cache_icache, cache_pcache), str ∈ entries0, entries0[str] ∈ cache_files, m3 ∈ cache_dirs, cache_sync → synced (cache_files[entries0[str], mkfile(m6, md0, m0, content)], cache_icache[entries0[str], mkientry(false, mkinode(entries0[str], md0, false, m0, 0, m6))] [m3, mkientry(false, mkinode(m3, md1, true, # links(m3, cache_dirs), m4, m9)) ], cache_pcache), cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m3, cache_dirs) ≠ ∅ ∨ m3 = ROOT_INO ⊦ ⟨afs_inode_sync#(mkinode(entries0[str], md0, false, m0 + 1, 0, m6); dirs, files); p_inode := (m3 ∈ dirs ⊃ mkinode(m3, dirs[m3].meta, true, dirs[m3].nlink, dirs[m3].nsubdirs, dirs[m3].size) ;mkinode(m3, files[m3].meta, false, files[m3].nlink, 0, files[m3].size) ); c_inode := getinode(entries0[str], dirs, files); err := ESUCCESS; asynced := ?⟩ ( dirs = cache_dirs[m3, mkdir(m9, md1, # links(m3, cache_dirs), m4, entries0 -- str)] ∧ files = (cache_files[entries0[str], mkfile(m6, md0, m0, content)] ⊕ cache_pcache) ⊕ cache_icache[entries0[str], mkientry(false, mkinode(entries0[str], md0, false, m0, 0, m6))] [m3, mkientry(false, mkinode(m3, md1, true, # links(m3, cache_dirs), m4, m9)) ] ∧ (asynced ↔ asynced0) ∧ mkinode(m3, md1, true, # links(m3, cache_dirs), m4, m9) = p_inode ∧ mkinode(entries0[str], md0, false, m0, 0, m6) = c_inode ∧ ESUCCESS = err), ino ∈ dirs, ino ∈ files

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

Additional information

Used simplifier rules: ⊦ ino ∈ dirs[ino0, ad] ↔ ino ∈ dirs; (s)% ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs → ¬ ino ∈ files; (s)% ⊦ ino ∈ files ⊕ pcache ↔ ino ∈ files; (s)% ⊦ ino ∈ files ⊕ icache ↔ ino ∈ files; (s)% ⊦ ino ∈ files[ino0, af] ↔ ino ∈ files; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)