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Proof step 84 from proof refine-evict (previous step)

cache_files[m].nlink = 0, 0 = ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m].nlink, 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_files, ¬ m ∈ cache_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ⟪icache_delete#(m; err, cache_icache); boolvar := false; if ¬ boolvar then pcache_evict#(m; err, cache_pcache)⟫ ⟨cache_dirs0 := cache_dirs; afs_evict#(mkinode(m, md, boolvar, 0, 0, m2), cache_asynced; err0, cache_dirs, afs_files)⟩ (cache_dirs = cache_dirs0 ∧ afs_files = ((cache_files -- m) ⊕ cache_pcache) ⊕ cache_icache ∧ err = err0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 85:
0 = ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m].nlink, cache_files[m] = mkfile(m0, md0, m1, content), 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_files, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ⟪icache_delete#(m; err, cache_icache); boolvar := false; if ¬ boolvar then pcache_evict#(m; err, cache_pcache)⟫ ⟨cache_dirs0 := cache_dirs; afs_evict#(mkinode(m, md, boolvar, 0, 0, m2), cache_asynced; err0, cache_dirs, afs_files)⟩ (cache_dirs = cache_dirs0 ∧ afs_files = ((cache_files -- m) ⊕ cache_pcache) ⊕ cache_icache ∧ err = err0), m = ROOT_INO, m ∈ cache_dirs

Rule argument

spec: abstract-file name: elim seq: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content) subst: [af, m, md, m0, content] → [cache_files[m], m0, md0, m1, content]

Additional information

Used simplifier rules: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content); (elim) Used terms: cache_files[m], m0, md0, m1, content