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Proof step 119 from proof refine-iget (previous step)

cache_icache[ino, mkientry(false, mkinode(ino, md, false, # links(ino, cache_dirs), 0, m))][ino0].inode = mkinode(m0, md0, true, m1, m2, m3), cache_files[ino] = mkfile(m, md, # links(ino, cache_dirs), content), cache_files[ino0] = mkfile(m4, md1, m5, content0), 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, false, # links(ino, cache_dirs), 0, m))], ino0 ∈ cache_files, ino ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[ino0] = mkfile(m4, md1, m5, content0 ⊕ mkcontent(ino0, cache_pcache)), ino ∈ cache_dirs, ino ∈ cache_icache

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 120:
cache_icache[ino, mkientry(false, mkinode(ino, md, false, # links(ino, cache_dirs), 0, m))][ino0].inode = mkinode(m0, md0, true, m1, m2, m3), cache_files[ino] = mkfile(m, md, # links(ino, cache_dirs), content), cache_files[ino0] = mkfile(m4, md1, # links(ino0, cache_dirs), content0), 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, false, # links(ino, cache_dirs), 0, m))], ino0 ∈ cache_files, ino ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[ino0] = mkfile(m4, md1, # links(ino0, cache_dirs), content0 ⊕ mkcontent(ino0, cache_pcache)), ino ∈ cache_dirs, ino ∈ cache_icache

Rule argument

Additional information

Used simplifier rules: afs-cons-file-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ files ∧ files[ino] = mkfile(m, md, n, content) → # links(ino, dirs) = n; (forward) from specification afs-base