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Proof step 58 from proof refine-lookup (previous step)

cache_dirs[p_ino] = mkdir(m, md, m0, m1, entries), err = ESUCCESS, 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), p_ino ∈ cache_dirs, dent0.name ∈ entries, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(p_ino, cache_dirs) ≠ ∅ ∨ p_ino = ROOT_INO ⊦ ⟪dcache_set#(p_ino, dent0.name, mkdentry(dent0.name, entries[dent0.name]); err, cache_dcache)⟫ ⟨dent1 := dent0; afs_lookup#(p_ino, cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache, cache_asynced; dent0, err0)⟩ (mkdentry(dent1.name, entries[dent1.name]) = dent0 ∧ err = err0), dentrykey(p_ino, dent0.name) ∈ cache_dcache

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: afs-cons-dir-nlink: ⊦ afs-cons(dirs, files) ∧ ino ∈ dirs ∧ dirs[ino] = mkdir(n0, md, n, n1, entries) → # links(ino, dirs) = n; (forward) from specification afs-base