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Proof step 101 from proof refine-iget (previous step)

cache_dirs[ino] = mkdir(m, md, # links(ino, cache_dirs), m1, entries), 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), ino0 ∈ cache_files, ino ∈ cache_dirs, ino0 ∈ cache_icache[ino, mkientry(false, mkinode(ino, md, true, # links(ino, cache_dirs), m1, m))], cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[ino0] = mkfile (cache_icache[ino, mkientry(false, mkinode(ino, md, true, # links(ino, cache_dirs), m1, m))][ino0].inode.size, cache_icache[ino, mkientry(false, mkinode(ino, md, true, # links(ino, cache_dirs), m1, m))][ino0].inode.meta, cache_icache[ino, mkientry(false, mkinode(ino, md, true, # links(ino, cache_dirs), m1, m))][ino0].inode.nlink, (cache_files ⊕ cache_pcache)[ino0].content), cache_icache[ino, mkientry(false, mkinode(ino, md, true, # links(ino, cache_dirs), m1, m))][ino0].inode.directory, ino ∈ cache_icache

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 102:
cache_dirs[ino] = mkdir(m, md, # links(ino, cache_dirs), m1, entries), 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), ino0 ∈ cache_icache[ino, mkientry(false, mkinode(ino, md, true, # links(ino, cache_dirs), m1, m))], ino ∈ cache_dirs, ino0 ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[ino0] = mkfile (cache_icache[ino, mkientry(false, mkinode(ino, md, true, # links(ino, cache_dirs), m1, m))][ino0].inode.size, cache_icache[ino, mkientry(false, mkinode(ino, md, true, # links(ino, cache_dirs), m1, m))][ino0].inode.meta, cache_icache[ino, mkientry(false, mkinode(ino, md, true, # links(ino, cache_dirs), m1, m))][ino0].inode.nlink, cache_files[ino0].content ⊕ mkcontent(ino0, cache_pcache)), cache_icache[ino, mkientry(false, mkinode(ino, md, true, # links(ino, cache_dirs), m1, m))][ino0].inode.directory, ino ∈ cache_icache

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)