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Proof step 406 from proof refine-write_inode (previous step)

cache_files[m] = mkfile(m2, md0, # links(m, cache_dirs), content0), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m0, md, m1, content), cache_icache[m] = mkientry(boolvar0, mkinode(m3, md1, boolvar, m4, m5, m6)), 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_files, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ m1 = # links(m, cache_dirs), m ∈ cache_icache ∧ ¬ boolvar, m ∈ cache_icache ∧ cache_icache[m].inode.directory

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 407:
cache_files[m] = mkfile(m2, md0, # links(m, cache_dirs), content0), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m0, md, m1, content), cache_icache[m] = mkientry(boolvar0, mkinode(m3, md1, boolvar, m4, m5, m6)), 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_files, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ m1 = # links(m, cache_dirs), m ∈ cache_icache ∧ ¬ boolvar, m ∈ cache_icache ∧ boolvar

Rule argument

Additional information

Used simplifier rules: ⊦ mkinode(m, md, boolvar, m0, m1, m2).directory ↔ boolvar; (s)% ⊦ mkientry(boolvar, inode).inode = inode; (s)