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Proof step 135 from proof refine-mkdir (previous step)

cache_files[ino] = mkfile(m10, md4, # links(ino, cache_dirs), content), cache_icache[m1, mkientry(false, mkinode(m1, md2, true, m3, m4, m))][m5, mkientry(false, mkinode(m5, md3, true, 1, 0, 0))][ino] = mkientry(boolvar, mkinode(m0, md, true, m2, m7, m9)), 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), ino ∈ cache_files, m1 ∈ cache_dirs, ino ∈ cache_icache[m1, mkientry(false, mkinode(m1, md2, true, m3, m4, m))][m5, mkientry(false, mkinode(m5, md3, true, 1, 0, 0))], ino ∈ cache_icache, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m1, cache_dirs) ≠ ∅ ∨ m1 = ROOT_INO ⊦ m5 = 0, mkfile(cache_icache[ino].inode.size, cache_icache[ino].inode.meta, cache_icache[ino].inode.nlink, (cache_files ⊕ cache_pcache)[ino].content) = mkfile(m10, md4, # links(ino, cache_dirs), content ⊕ mkcontent(ino, cache_pcache)), cache_icache[ino].inode.directory, str ∈ entries1, m5 ∈ cache_files, m5 ∈ cache_dirs

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 136:
cache_files[ino] = mkfile(m10, md4, # links(ino, cache_dirs), content), cache_icache[m1, mkientry(false, mkinode(m1, md2, true, m3, m4, m))][m5, mkientry(false, mkinode(m5, md3, true, 1, 0, 0))][ino] = mkientry(boolvar, mkinode(m0, md, true, m2, m7, m9)), 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), ino ∈ cache_files, m1 ∈ cache_dirs, ino ∈ cache_icache[m1, mkientry(false, mkinode(m1, md2, true, m3, m4, m))][m5, mkientry(false, mkinode(m5, md3, true, 1, 0, 0))], ino ∈ cache_icache, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m1, cache_dirs) ≠ ∅ ∨ m1 = ROOT_INO ⊦ m5 = 0, mkfile(cache_icache[ino].inode.size, cache_icache[ino].inode.meta, cache_icache[ino].inode.nlink, content ⊕ mkcontent(ino, cache_pcache)) = mkfile(m10, md4, # links(ino, cache_dirs), content ⊕ mkcontent(ino, cache_pcache)), cache_icache[ino].inode.directory, str ∈ entries1, m5 ∈ cache_files, m5 ∈ cache_dirs

Rule argument

Additional information

Used simplifier rules: ⊦ mkfile(m, md, m0, content).content = content; (s)%⊦ (files ⊕ pcache)[ino] = mkfile (files[ino].size, files[ino].meta, files[ino].nlink, files[ino].content ⊕ mkcontent(ino, pcache)); (s)