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Proof step 251 from proof refine-write_inode (previous step)

cache_files[m] = mkfile(m3, md0, m4, content), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m5, md1, m6, content0), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, cache_dirs0 = cache_dirs, 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), ⌊err0⌋ , cache_sync → synced(cache_files, cache_icache, cache_pcache), m ∈ cache_dirs ∧ m0 = cache_dirs[m].nlink ∧ m2 = cache_dirs[m].size ∧ m1 = cache_dirs[m].nsubdirs ∧ boolvar ∨ m ∈ cache_files ∧ m0 = m6 ∧ m1 = 0 ∧ ¬ boolvar, cache_sync ∨ boolvar, m ∈ cache_dirs ∧ m0 = cache_dirs[m].nlink ∧ m2 = cache_dirs[m].size ∧ m1 = cache_dirs[m].nsubdirs ∧ boolvar ∨ m ∈ cache_files ∧ m0 = m4 ∧ m1 = 0 ∧ ¬ boolvar ⊦ ⟨afs_write_inode#(mkinode(m, md, boolvar, m0, m1, m2); err1, cache_dirs, afs_files; afs_asynced)⟩ (cache_dirs = cache_dirs0 ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ asynced) ∧ err0 = err1)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 252:
((cache_files ⊕ cache_pcache) ⊕ cache_icache)[m] = mkfile(m5, md1, m6, content0), cache_files[m] = mkfile(m3, md0, m4, content), cache_dirs[m] = mkdir(m7, md2, m8, m9, entries), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, cache_dirs0 = cache_dirs, 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), ⌊err0⌋ , cache_sync → synced(cache_files, cache_icache, cache_pcache), m ∈ cache_dirs ∧ m0 = m8 ∧ m2 = m7 ∧ m1 = m9 ∧ boolvar ∨ m ∈ cache_files ∧ m0 = m4 ∧ m1 = 0 ∧ ¬ boolvar, cache_sync ∨ boolvar, m ∈ cache_dirs ∧ m0 = m8 ∧ m2 = m7 ∧ m1 = m9 ∧ boolvar ∨ m ∈ cache_files ∧ m0 = m6 ∧ m1 = 0 ∧ ¬ boolvar ⊦ ⟨afs_write_inode#(mkinode(m, md, boolvar, m0, m1, m2); err1, cache_dirs, afs_files; afs_asynced)⟩ (cache_dirs = cache_dirs0 ∧ afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ asynced) ∧ err0 = err1)

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], m7, md2, m8, m9, 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], m7, md2, m8, m9, entries