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Proof step 409 from proof refine-write_inode (previous step)

cache_files[m] = mkfile(m2, md0, # links(m, cache_dirs), content0), mkfile(cache_icache[m].inode.size, cache_icache[m].inode.meta, cache_icache[m].inode.nlink, (cache_files ⊕ cache_pcache)[m].content) = mkfile(m0, md, m1, content), 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, m ∈ cache_icache, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ m1 = # links(m, cache_dirs), cache_icache[m].inode.directory

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 410:
cache_files[m] = mkfile(m2, md0, # links(m, cache_dirs), content0), 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, m ∈ cache_icache, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ cache_icache[m].inode.nlink = # links(m, cache_dirs), cache_icache[m].inode.directory

Rule argument

Additional information

Used simplifier rules: ⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0; (ws)% ⊦ 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)