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Proof step 19 from proof refine-evict (previous step)

cache_dirs[m].nlink = 0, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, err = ESUCCESS, m ≠ ROOT_INO, 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), m ∈ cache_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ⟪icache_delete#(m; err, cache_icache); boolvar := true; if ¬ boolvar then pcache_evict#(m; err, cache_pcache)⟫ ⟨cache_dirs0 := cache_dirs; afs_evict#(mkinode(m, md, boolvar, 0, cache_dirs[m].nsubdirs, cache_dirs[m].size), cache_asynced; err0, cache_dirs, afs_files)⟩ (cache_dirs = cache_dirs0 -- m ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ err = err0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 20:
cache_dirs[m] = mkdir(m0, md0, m1, m2, entries), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, err = ESUCCESS, m1 = 0, 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), m ∈ cache_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ⟪icache_delete#(m; err, cache_icache); boolvar := true; if ¬ boolvar then pcache_evict#(m; err, cache_pcache)⟫ ⟨cache_dirs0 := cache_dirs; afs_evict#(mkinode(m, md, boolvar, 0, m2, m0), cache_asynced; err0, cache_dirs, afs_files)⟩ (cache_dirs = cache_dirs0 -- m ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ err = err0), m = ROOT_INO

Rule argument

spec: abstract-dir name: elim seq: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries) subst: [ad, m, md, m0, m1, entries] → [cache_dirs[m], m0, md0, m1, m2, entries]

Additional information

Used simplifier rules: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries); (elim) Used terms: cache_dirs[m], m0, md0, m1, m2, entries