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Proof step 56 from proof refine-write_inode (previous step)

cache_dirs[m] = mkdir(m0, md2, # links(m, cache_dirs), m6, entries0), cache_icache[m] = mkientry(boolvar, mkinode(m1, md1, boolvar0, m2, m4, m5)), 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), m ∈ cache_dirs, m ∈ cache_icache, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ∀ ino. ( ino ∈ (cache_files ⊕ cache_pcache) ⊕ cache_icache ↔ ino ∈ (cache_files ⊕ cache_pcache) ⊕ cache_icache[m1, mkientry(false, mkinode(m1, md, boolvar0, m2, m4, m5))]) ∧ ( 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, md, boolvar0, m2, m4, m5))])[ino])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 57:
cache_icache[m] = mkientry(boolvar, mkinode(m1, md1, boolvar0, m2, m4, m5)), cache_dirs[m] = mkdir(m0, md2, # links(m, cache_dirs), m6, 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), m ∈ cache_icache, m ∈ cache_dirs, ino ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[ino] = ((cache_files ⊕ cache_pcache) ⊕ cache_icache[m1, mkientry(false, mkinode(m1, md, boolvar0, m2, m4, m5))])[ino]

Rule argument

Additional information

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