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Proof step 413 from proof refine-rename-file-negdentry (previous step)

cache_dirs[m3] = mkdir(m0, md4, # links(m3, cache_dirs), m2, entries0), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries0[str]] = mkfile(m9, md2, m11, content), cache_dirs[m] = mkdir(m8, md3, # links(m, cache_dirs), m13, entries), cache_files[entries0[str]] = mkfile(m1, md1, m4, 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), str ∈ entries0, m3 ∈ cache_dirs, entries0[str] ∈ cache_files, m ∈ cache_dirs, m = m3 → md = md0, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m3, cache_dirs) ≠ ∅ ∨ m3 = ROOT_INO, links(m, cache_dirs) ≠ ∅ ∨ m = ROOT_INO ⊦ m11 = m4, str0 ∈ entries

Heuristic simplifier applied rule simplifier

And obtained the following new goals

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