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Proof step 84 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, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[ino0] = ((cache_files ⊕ cache_pcache) ⊕ cache_icache[ino, mkientry(false, mkinode(ino, md, true, # links(ino, cache_dirs), m1, m))])[ino0], ino ∈ cache_icache, ino0 ∈ cache_icache[ino, mkientry(false, mkinode(ino, md, true, # links(ino, cache_dirs), m1, m))] ∧ ¬ cache_icache[ino, mkientry(false, mkinode(ino, md, true, # links(ino, cache_dirs), m1, m))][ino0].inode.directory

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 85:
cache_dirs[ino] = mkdir(m, md, # links(ino, cache_dirs), m1, entries), cache_icache[ino, mkientry(false, mkinode(ino, md, true, # links(ino, cache_dirs), m1, m))][ino0].inode.directory, 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_files[ino0].size, cache_files[ino0].meta, cache_files[ino0].nlink, cache_files[ino0].content ⊕ mkcontent(ino0, cache_pcache)), ino ∈ cache_icache

Rule argument

Additional information

Used simplifier rules: ⊦ ino ∈ icache ∧ icache[ino].inode.directory → (files ⊕ icache)[ino] = files[ino]; (s)% ⊦ ino ∈ icache[ino0, ie] ↔ ino = ino0 ∨ ino ∈ icache; (ws)%⊦ (files ⊕ pcache)[ino] = mkfile (files[ino].size, files[ino].meta, files[ino].nlink, files[ino].content ⊕ mkcontent(ino, pcache)); (s)% ⊦ ¬ ino ∈ icache → (files ⊕ icache)[ino] = files[ino]; (s)