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Proof step 115 from proof refine-mkdir (previous step)

cache_dirs[m1] = mkdir(m6, md1, # links(m1, cache_dirs), m8, entries1), (cache_dirs[m1, mkdir(m6 + 1, md1, # links(m1, cache_dirs), m8 + 1, entries1[str, m5])] ++ m5)[m1] = mkdir(m, md0, m3, m4, entries0), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), afs-cons(cache_dirs, cache_files), 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), m1 ∈ cache_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m1, cache_dirs) ≠ ∅ ∨ m1 = ROOT_INO ⊦ m5 = 0, str ∈ entries1, m5 ∈ cache_files, m5 ∈ cache_dirs, ∀ ino. ( ino ∈ (cache_files ⊕ cache_pcache) ⊕ cache_icache ↔ ino ∈ (cache_files ⊕ cache_pcache) ⊕ cache_icache[m1, mkientry(false, mkinode(m1, md2, true, m3, m4, m))][m5, mkientry(false, mkinode(m5, md3, true, 1, 0, 0))]) ∧ ( ino ∈ (cache_files ⊕ cache_pcache) ⊕ cache_icache → ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[ino] = ( (cache_files ⊕ cache_pcache) ⊕ cache_icache[m1, mkientry(false, mkinode(m1, md2, true, m3, m4, m))][m5, mkientry(false, mkinode(m5, md3, true, 1, 0, 0))] )[ino ])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 116:
(cache_dirs[m1, mkdir(m6 + 1, md1, # links(m1, cache_dirs), m8 + 1, entries1[str, m5])] ++ m5)[m1] = mkdir(m, md0, m3, m4, entries0), cache_dirs[m1] = mkdir(m6, md1, # links(m1, cache_dirs), m8, entries1), 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), m1 ∈ cache_dirs, ino ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m1, cache_dirs) ≠ ∅ ∨ m1 = ROOT_INO ⊦ ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[ino] = ( (cache_files ⊕ cache_pcache) ⊕ cache_icache[m1, mkientry(false, mkinode(m1, md2, true, m3, m4, m))][m5, mkientry(false, mkinode(m5, md3, true, 1, 0, 0))] )[ino ], m5 = 0, m5 ∈ cache_dirs, m5 ∈ cache_files, str ∈ entries1

Rule argument

Additional information

Used simplifier rules: ⊦ ino ∈ files ⊕ pcache ↔ ino ∈ files; (s)% ⊦ ino ∈ files ⊕ icache ↔ ino ∈ files; (s)