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Proof step 444 from proof refine-evict (previous step)

((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m0, md0, cache_files[m].nlink, content), afs_dirs = cache_dirs, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, cache_files[m].nlink ≠ 0, m ≠ ROOT_INO, 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, ¬ m ∈ cache_dirs, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ⟨afs_evict#(mkinode(m, md, false, cache_files[m].nlink, 0, m2), cache_asynced; err0, afs_dirs, afs_files)⟩ (afs_dirs = cache_dirs ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ ESUCCESS = err0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 445:
((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m0, md0, m3, content), cache_files[m] = mkfile(m1, md1, m3, content0), afs_dirs = cache_dirs, afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, 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, cache_sync → synced(cache_files, cache_icache, cache_pcache) ⊦ ⟨afs_evict#(mkinode(m, md, false, m3, 0, m2), cache_asynced; err0, afs_dirs, afs_files)⟩ (afs_dirs = cache_dirs ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ ESUCCESS = err0), m = ROOT_INO, m3 = 0, 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], m1, md1, m3, content0]

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], m1, md1, m3, content0