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Proof step 225 from proof refine-write_inode (previous step)

cache_files[m] = mkfile(m0, md0, # links(m, cache_dirs), content), cache_icache[ino] = mkientry(boolvar0, mkinode(m1, md1, boolvar, m3, 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), synced(cache_files, cache_icache, cache_pcache), ino ∈ cache_files, m ∈ cache_files ⊦ (ino = m ⊃ mkfile(m2, md, # links(m, cache_dirs), content ⊕ mkcontent(m, cache_pcache));((cache_files ⊕ cache_pcache) ⊕ cache_icache)[ino]) = ((cache_files[m, mkfile(m2, md, # links(m, cache_dirs), content)] ⊕ cache_pcache) ⊕ cache_icache)[ino], m ∈ cache_icache, ino ∈ cache_icache ∧ ¬ boolvar, ino ∈ cache_icache ∧ cache_icache[ino].inode.directory

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 226:
cache_files[m] = mkfile(m0, md0, # links(m, cache_dirs), content), cache_icache[ino] = mkientry(boolvar0, mkinode(m1, md1, boolvar, m3, 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), synced(cache_files, cache_icache, cache_pcache), ino ∈ cache_files, m ∈ cache_files ⊦ (ino = m ⊃ mkfile(m2, md, # links(m, cache_dirs), content ⊕ mkcontent(m, cache_pcache));((cache_files ⊕ cache_pcache) ⊕ cache_icache)[ino]) = ((cache_files[m, mkfile(m2, md, # links(m, cache_dirs), content)] ⊕ cache_pcache) ⊕ cache_icache)[ino], m ∈ cache_icache, ino ∈ cache_icache ∧ ¬ boolvar, ino ∈ 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)