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Proof step 53 from proof refine-write_inode (previous step)

# links(m, cache_dirs) = m3, cache_dirs[m] = mkdir(m0, md0, m3, m6, entries), cache_icache[m] = mkientry(boolvar, mkinode(m1, md1, boolvar0, m2, m4, m5)), cache_dirs[m] = mkdir(m0, md2, m3, m6, entries0), 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) ⊦ (cache_files ⊕ cache_pcache) ⊕ cache_icache = (cache_files ⊕ cache_pcache) ⊕ cache_icache[m1, mkientry(false, mkinode(m1, md, boolvar0, m2, m4, m5))]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 54:
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, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ (cache_files ⊕ cache_pcache) ⊕ cache_icache = (cache_files ⊕ cache_pcache) ⊕ cache_icache[m1, mkientry(false, mkinode(m1, md, boolvar0, m2, m4, m5))]

Rule argument

Additional information

Used simplifier rules: ⊦ mkdir(m, md, m0, m1, entries) = mkdir(m2, md0, m3, m4, entries0) ↔ m = m2 ∧ md = md0 ∧ m0 = m3 ∧ m1 = m4 ∧ entries = entries0; (ws)