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Proof step 13 from proof refine-unlink (previous step)

((cache_files ⊕ cache_pcache) ⊕ cache_icache)[cache_dirs[m].entries[str]] = mkfile(m0, md, m1, content), cache_files[cache_dirs[m].entries[str]] = mkfile(m2, md0, m3, 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), cache_dirs[m].entries[str] ∈ cache_files, str ∈ cache_dirs[m].entries, m ∈ cache_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ m1 = m3

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
((cache_files ⊕ cache_pcache) ⊕ cache_icache)[cache_dirs[m].entries[str]] = mkfile(m0, md, m1, content), cache_files[cache_dirs[m].entries[str]] = mkfile(m2, md0, # links(cache_dirs[m].entries[str], 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), cache_dirs[m].entries[str] ∈ cache_files, str ∈ cache_dirs[m].entries, m ∈ cache_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ m1 = # links(cache_dirs[m].entries[str], cache_dirs)

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